Five cool things about Mr. Rook:

His downside is secretly an upside. You draw your weaknesses for free alongside other cards rather than having to draw them later in place of another card. He grants you a significant amount of control over when you draw your weaknesses.

He is expendable. Unlike a certain professor of entomology, Mr. Rook works quickly. He is two health and sanity worth of soak, and if you spend a secret every turn you are happy to use up that soak two turns after you play him. He doesn't stop you putting other allies in your deck or force you to run Charisma. Which lead on to...

He is great with Calling in Favors. I had a game where I put Mr Rook into play four times and still had Mr Rook in my hand.

When you have nine or fewer cards left in your deck he lets you search the whole thing. It's like he hands you a No Stone Unturned (5) that costs zero at the start of the round.

When you draw a treachery with a skill test he can instantly search your deck for relevant icons. There is a player window in every skill test just before cards are committed.

Here's a bonus sixth thing: If your random weakness is Doomed you will live fast, die young, and start earning experience with your replacement investigator much sooner than you would otherwise.

Out of curiosity, I decided to pick apart each basic weakness in the game, and how effective Rook is at mitigating the timing of them:

Core Set

Amnesia - This one could go either way. If you have Amnesia in your deck, you should aim to play the assets you can before playing Rook. If you expect to draw lots of cards (and since you have access to Rook you likely do), the earlier this is played the better. Take note of when Higher Education needs to be online for you, and figure out when best to time Amnesia. If the 1 card left in your hand is Cryptic Research, you should be alright.

Paranoia - Already one of the most benign weaknesses, but with Rook it's trivial. Extra points for playing Rook with exactly 3 resources left in the pool.

Haunted, Psychosis, and Hypochondria - Action 1: play Rook; Action 2&3, goodbye weakness. Not a bad opening play at all, or anytime you have an extra turn to deal with it. Rook definitely helps with these.

Mob Enforcer - Best played right after an Emergency Cache to help Parley him effectively. Great timing here.

Silver Twilight Acolyte - Best played after you get some weapons out. You can also time this on a round the agenda would advance anyway to mitigate the doom for 1 round. Definitely be cautious about this one- it could be a short scenario if you happen to whiff on killing this guy. Low combat investigators should probably keep this one buried as long as possible, especially if playing solo.

Stubborn Detective - As above, make sure you have a weapon for this guy. Joe Diamond and Roland Banks can maybe afford to be a bit riskier with him (fitting, as they are stubborn detectives themselves). Be cautious with Finn Edwards, as he can more easily evade the detective and can probably even generate some Pickpocketing economy with him, but will lose the free evade action each turn. I'd say for low combat solo investigators you're better off keeping the Detective buried as long as you can- even evasive investigators don't want this guy chasing them all scenario long.

Dunwich Legacy

Indebted - Obviously this doesn't go in your deck, so Rook can't mitigate this at all. This means that if you draw a weakness, it'll always be your investigator specific one until a scenario makes you add an extra weakness to your deck. Downside here is no choice from drawing 2 weaknesses at once, but the upside is you only have to prepare for one possible weakness every time.

Internal Injury and Chronophobia - See above for the equivalent Core Set two action weaknesses.

Through the Gates - By drawing it early you wont get blindsided if the top card of the library happens to be some important asset you have in play (e.g. Lightning Gun). The only other way to make use of the timing on this is to set up the top card of your library. Something like Scroll of Secrets for example could really help here.

Path to Carcosa

Overzealous - No one likes drawing two encounter cards, even if they get to choose when it happens. This one depends heavily on the investigator and the player count. If you have the opportunity to be in the vicinity of other investigators who can commit to tests, then play Rook. If you're playing solo and the encounter deck is full of enemies, then Roland Banks can actually get some value from this, though he'll still probably have at least one skill check out of the two cards. If on the other hand you have an encounter deck full of Hexes and Terrors, and you happen to be Finn Edwards, you don't play Rook unless you have a stockpile of Guts and Logical Reasoning.

Drawing the Sign - See above for the equivalent Core Set two action weaknesses.

The Thing That Follows - This one should be kept buried as long as possible, so Rook doesn't help here.

Unspeakable Oath (Bloodthirst), Unspeakable Oath (Curiosity), and Unspeakable Oath (Cowardice) - These weaknesses are so tame already for anyone able to take Rook. If you're a Seeker you might have some trouble triggering Bloodthirst or Cowardice, but the actually downside of having a hidden card clogging up your hand early is rarely a pressing issue. Generally it makes sense to draw into these early to maximize your ability to resolve them before the end of the scenario, so Rook helps quite a lot here.

The Forgotten Age

Dark Pact - You definitely don't want to draw into Dark Pact ever, no amount of timing really helps with it since it's not a Revelation based weakness. You can't mitigate the doom on The Price of Failure either, so at best you can use Rook to time the damage so that you have time to heal it instead of being assaulted all at once towards the end of a scenario. Overall though I'd say Rook hurts more than he helps this one. EDIT: Well, just take the two damage onto Rook and call it a day. Could be worse, definitely not that bad of a weakness overall.

Doomed - I love the idea that you can use Rook to kill your investigator faster and start fresh. Draw Doomed twice in scenario 1, draw into Accursed Fate twice in scenario 2, then The Bell Tolls in scenario 2 or 3, starting fresh in scenario 3 or 4. It might even be faster than that, I'm not sure- getting to the death card in scenario 1 seems very unlikely to me though. Some people will get a kick out of that, but at the end of the day if you're trying to mitigate your basic weakness, Rook is the single worst thing you could do for yourself.

The Circle Undone

The 13th Vision - See above for the equivalent two action Core Set weaknesses.

The Tower • XVI - Definitely similar to Mob Enforcer. Make sure you have the resources to pay for this: 3 for Rook, 4 for the Tower, so 7 total. I would argue that Rook is slightly less effective here since you can't shuffle away The Tower when you draw your opening hand, so there's a good chance that you'll deal with it turn 1 action 1 anyway.

The Dream Eaters

Narcolepsy - You should make sure you Rook at the very end of your turn (or during someone else's turn), before you get locked into doing nothing. Chances are someone is nearby to wake you up and can spare an action to do so. Or if you know you're going to be hit for damage/horror somehow anyway, you could grab this with Rook and break it yourself. This is one you have to be somewhat mindful of timing wise, but overall it's quite tame.

Self-Centered - Yet another "2 action: discard" weakness. Rook is great for these to begin with, but this one is particularly benign if you're far from the group anyway. Be cautious about your actions and make sure you either have the actions to kill it or you don't need to help anybody in the immediate future.

Your Worst Nightmare - Similar to Narcolepsy, this one is best triggered if you know someone else is nearby to deal with it. It should be noted however that you are allowed to Evade your nightmares. Particularly useful knowledge for Finn Edwards or Ursula Downs, or even Mandy Thompson with some access.

Kleptomania - Okay, this one is the weirdest. There could be a situation where someone else has something you want (usually resources, but maybe those Track Shoes are looking good?), in which case you could actively use Rook just to be able to steal their stuff. That's wild. So yeah, that's a thing. Otherwise it's a recursive weakness so it's one that's going to be very annoying to use with Rook unless you're willing to let it sit and tank some horror.

Final Thoughts

Overall I'd say Rook definitely helps mitigate most of the basic weaknesses in the game. There are some where Rook is less helpful than you'd like him to be for the Opportunity Cost of putting him in your deck, and there are a couple that are actually much worse if drawn early. Cards like No Stone Unturned and Eureka! are probably better suited for drawing the cards you need without triggering such a weakness. Of course none of this matters much if you're building a combo based deck- Rook is the man for decks that need a specific card or set of cards to work.

Bonus Round: Notable Investigator Specific Weaknesses

Cover Up - Always better drawn early than late. Roland loves Rook.

Rex's Curse - This one should be kept buried as long as possible since it gets shuffled back in anyway. Rex hates Rook.

Searching for Izzie - My goodness this one is such a pain to complete unless it's drawn early. Jenny loves Rook. Just be mindful of the locations in play and make sure you don't block yourself off from wherever it should land (e.g. locations that say "You can't move into X" which need their effect taken away somehow late in the scenario).

The King in Yellow - Stockpile on skill cards, then play Rook. Definitely better than being caught off guard after an important skill check.

Crisis of Identity - If you play Rook and he draws into this, you have to discard Rook from play along with any other Seeker cards, which honestly isn't so bad- 3 resources and 1 card to grab a card you really need and cancel a Crisis is still good. So obviously you want to do this earlier rather than later, as in before all the Seeker assets end up in play. Also, since there's two Crises in the deck, you have a much higher chance of drawing one along with your basic weakness, so if your basic weakness is really terrible, there's less risk when playing him. Lola is also the kind of investigator who benefits from draw and tutoring effects, so Rook is well suited for her.

Unsolved Case - Again, a lot like Indebted. You'll only have your basic weakness in your main deck, so you only have to prepare for that one weakness when playing Rook (still keeping 1 resource on reserve to pay for Unsolved Case next turn should it come up).

Mr. "Rook" flew under my radar until I tried to use it and realized how strong he is.

You basically get 3 uses of a better No Stone Unturned for 3 resources, this is just great. And, as other reviews put it, drawing your weakness early is actually often an upside. On top of that, you still get to draw a card even when you find your weakness, when normally drawing your weakness would rob you of one card. In the rare situations that you really do not want to risk drawing your weakness and thus can't use Mr. Rook's ability, or when he's out of charges, he still makes a more than decent meat shield with a 2/2 body, the additional health being of a particular note for a Seeker ally.

To further develop on the review analyzing each basic weakness, let's analyze more in depth each investigator's signature weakness and see how using Rook will affect this investigator in this context: how bad (or good) it is to draw your weakness, and (where appropriate) what could you fish in your deck to reduce the severity of your weakness. The review will thus not focus on whether Rook is worth the deck slot and should be selected instead of other cards (like a Dunwich investigator's wild slot) as this would make for a much larger review and would depend too much on deckbuilding.

Seeker

• Daisy Walker - The Necronomicon - Though Daisy's weakness would rob her of one of hands, maybe at the worst possible moment, her capabilities often largely ofset this issue. WIth a 5 , she does not rely on Magnifying Glass and isn't really using her hands for anything but books. Besides, as she gets only 1 free action per turn for using books, she tends not to run 2 in her decks, so in the end losing a hand is never really an issue. On top of that, her ability is nice but not great, and changing it into an token does not significantly decrease your chance of passing tests. Drawn early, you will probably have time to clear the The Necronomicon should you wish to do so, and drawn late your chances are high that it will not make you fail any test. My experience with Daisy is that she will often run two Old Book of Lore (or sometimes Encyclopedia) and no other hand asset, making her weakness moot and she will simply ignore it if she draws it. Considering the very low impact of this weakness, drawing it never really is an issue and you can be free to use Mr. "Rook" without fear. Should you wish to try so, Rook may even open alternatives deckbuilding strategies. Indeed, you could run other hand assets without risking of losing them as you would draw The Necronomicon earlier in scenarios and would just have to clean it and be rid of it, or you could search for Daisy's Tote Bag (a card that you can't really rely on when playing without Rook and most often ending up being committed for its icons) to solve any potential issue.
• Joe Diamond - Unsolved Case - Great news, Joe has one less weakness than everyone in his deck as Unsolved Case is part of his hunch deck. You can use and abuse Rook with very little drawback!
• Minh Thi Phan - The King in Yellow - Make sure you can ace a test and have 3 cards to spare, and fish for your weakness. Though you'll probably have to do some set up before being able to use Rook's ability with impunity.
• Norman Withers - Vengeful Hound - Like Min, you may have to do some set up to make sure that you are ready to fight your weakness, but when you are you will be free to use Rook's ability.
• Rex Murphy - Rex's Curse - Nope, you absolutely don't want Rook in a deck where the weakness is recursive!
• Ursula Downs - Call of the Unknown - Same as Rex - don't use Rook when you have a recursive weakness.

Survivors

• "Ashcan" Pete - Wracked by Nightmares. Play your first action exhausting Duke, search your deck with Mr. "Rook" and draw Wracked by Nightmares, and use your final two actions to get rid of it. Voila.

Mystics

• Jim Culver - Final Rhapsody - Jim's weakness if often not worse drawn early than late. If drawn early, at least you'll know exactly with how many damages you have to deal with, while if you have not drawn it you can never be sure of how many sanity/health points you really have left.
• Marie Lambeau - Baron Samedi - On one hand, when fatality count is high, you wouldn't be able to use Rook's ability. On the other hand, and much more interestingly, when fatality count is low, you could safely draw the Baron and get rid of it, while maybe fishing for Mystifying Song to give you even a little bit more time. This actually makes Marie's weakness more manageable.

Guardians

• Carolyn Fern - Rational Thought – Drawn early, Carolyn’s weakness may drop your set up to a slug, while when drawn late it’s impact on the scenario is often negligible. Sure, Rook, can you help finding your horror healing cards, but you won’t be able to pile on resources and even getting rid of Rational Thought when drawn too early may prove difficult.
• Roland Banks - Cover Up – Roland’s weakness is MUCH better drawn early as it will be a lot easier to get rid of it. Getting this weakness near the end of a Scenario is nearly a guaranteed trauma. Thus, Rook would be an excellent pick early, but his ability could be useless when the end of the scenario comes closer, though Roland decks sometimes mitigate their weakness with Forewarned, Quick Study or Dr. William T. Maleson.
• Zoey Samaras - Smite the Wicked - same as Roland, Zoey's weakness is a lot more manageable when drawn early, but is awful late. Rook is thus excellent early, but his ability will probably not be unusable late if you haven't seen your weakness yet. The weakness can be mitigated through Elusive, which Rook can help you to find.

Rogues

• Finn Edwards - Caught Red-Handed - though Finn's weakness is only "semi" recursive, the risk is high that it hits you several times in a scenario (by readying non-hunter enemies or a hunter enemy at your location and thus still returning into the deck). Though when no ennemy are around, Rook can be used with impunity! Still, I really dislike using Rook when I have a recursive weaknesses.
• Jenny Barnes - Searching for Izzie - Like Roland and Zoey, Jenny's weakness is a lot easier to deal with if you draw it early, but disastrous late, though here again fishing Elusive can be of great help.

Neutrals

• Lola Hayes - Crisis of Identity - Not only is Lola's weakness a real nightmare, drawing it with Rook means that you are in a role and will immediately have to discard related assets, including Mr. "Rook". It may also greatly mess up your plans depending on which role you intended to spend your round on. Contrary to the other review, I believe Rook definitly does not fit in a Lola deck, the tempo hit is way too heavy.

Bug card!

If you have already drew all of your weakness, it's a 2-2 ally cost 3 and 0xp but provide 3 search 9 for 1 effect, bug card.

if you still have some weakness in your deck, so what? For my experience, about 80% game I can draw all my weakness.So eventually it's almost same weither you use Rook or not. Is draw weakness early or on a specific time a bad thing? It's right for some weakness like Amnesia. But for most weakness I don't think so, because it means your is controllable, it won't appear on a inappropriate time that bother your crucial plan.

Rules clarification

Rules answer from FFQ: All aspects of an effect have timing priority over all "after..." triggering conditions that might arise as a consequence of that effect. (For example, if an effect reads "Gain 3 resources and draw 3 cards," resolve both aspects of the effect (gaining resources and drawing cards) before initiating an ability that reads "After drawing a card...")

So if you draw a weakness that interacts with your deck like Through the Gates or The Harbinger, you shuffle your deck before those effects take place.