The whole movies is full of internal holes, as well as external discrepancies with other Treks (the latter I'm inclined to forgive, since I don't think researching every series was halfway realistic even before TNG's many spinoffs). As well as just general scripted sloppiness.
First Uhura stupidly asks whether the "energy surge" they detected might've come from Kronos One. This comes literally seconds after Scotty dismissed the notion that Kronos One fired on itself (I'd like to see what that would even look like).
Chekov rightly points out the assassins could have beamed aboard Kronos One from this cloaked ship they've speculated exists. In fact he seems sure of it for some reason. Spock counters that someone aboard Enterprise needed to either fire the torpedoes or alter the ship's data banks. Having considered BOTH possibilities, he still doesn't consider the assassins could be anyone other than whoever tampered with the ship's weapon systems. In fact he stubbornly refuses to consider it, insisting the gravity boots ARE still aboard Enterprise.
Spock has the ship's garbage bin searched in case the assassins tried to get rid of their incriminating footwear, surmising the boots will stick to their users like "tiberian bats." And yet everyone acts like they're back to square one once they actually recover the boots but can't pin them to whoever's locker they were concealed in.
Spock dismisses the idea that the assassins would've thrown the boots out an airlock for "all to see." How is this? Is someone going to walk by a window and happen to see them? Are they going to float back to the ship and attach to its hull? (Is the ship moving or stationary?) I think in the TNG world, the boots would pop up on Worf's or Data's sensors. But Nick Meyer's version of ST is VERY far from the TNG world. I think if the boots attached to the ship, they might actually remain unnoticed until it returned to port. Assuming they didn't drift off the hull once the ship started moving again.
Once they find traces of klingon blood, Chekov wants to fly back to Starfleet. NO Chekov: you've just proved the assassins did in fact not only beam over from Enterprise but returned to it as well. ("Hey Starfleet, the assassins beamed over from our ship!" ... "You don't say.") If returning to Starfleet were an option Spock should've done so already.
What happens if you fire a phaser aboard a starship in the TNG world? Does a light flash on Worf's console? Does "nothing" happen? (my default assumption would be that both scenarios have been shown to be true

. If I re-watched all episodes I'd never remember to look for this specifically. I wouldn't hold this movie accountable either way).
What is "Interstellar Law"? Is it a Federation thing? Or something else? In almost any other version of ST (most notably Berman Trek) such a term would automatically be assumed to be a Federation thing. Christopher Plummer and John Schuck both seem to sneer as though it's a Federation thing. Are the klingons bound by it? And if they're not, can they really invoke it? On what terms do they get to hold Kirk and McCoy within their boarders and try them within their courtroom, as opposed to say, a more neutral site? Don't the klingons want everyone else who's accountable? Wouldn't they look like schmucks for settling on the two people that happen to already be within their grasp? Isn't that cowardly and weak behavior? Wouldn't that make the prosecution case against McCoy seem arbitrary, as if the court might've had to build an entirely different case had Spock beamed over instead? Do they want the peace process to proceed? Which side is the more desperate for peace, and therefore in the weaker position to negotiate for it? Does the Federation look like chumps for going along with this nonsense to keep the peace? Were the conspirators disappointed when they did?
Are there no other klingon ships between the Neutral Zone and Rura Penthe? Between the Neutral Zone and Khitomer? (Or did Enterprise stick wound inside Klingon space the whole while Spock was meld-interrogating Valeris?) Can you really cross over just by faking klingonese over radio to a listening post? In the TOS and TNG worlds, didn't the Romulans (it being a Romulan Neutral Zone in both those versions of ST) automatically intercept you the moment you crossed?
Camp Khitomer doesn't have a magnetic anti-transporter shield even though Rura Penthe does? They've scheduled a peace conference. One president has already been assassinated to try and stop the conference.
And people insist on finding problems with the 2009 movie?
(This is still my 4th favorite ST film, behind the 2009 movie. Feeling the need to pop in some Cliff Eidelman after typing all this).