Factual error: The whole basis of the trial and conviction of Cameron Poe is a crock. The judge can not arbitrarily mete out a sentence that is harsher based on the ability of someone to defend him/herself. In justifying the harsher sentence because of Poe's military skills, the judge effectively says that Poe is more guilty than an average person due to his honorable and decorated service in uniform to his country. In my entire time in law school, I never read one out of the literally hundreds of cases I was assigned in which a judge issued a harsher sentence because of someone's innate or learned abilities to defend themselves. But since this was a movie court room proceeding, the fact that Poe had a witness to the fight (his wife), the fact that he was injured in the fight, and the fact that his uniform was torn and otherwise ruined as a result of the fight are never examined. A D.A. wouldn't have taken this to a grand jury on a bet, because they would have never returned an indictment or "true bill."
Deliberate mistake: Leaven spends too much time thinking about if 645 and 372 are prime numbers to be believable. But she knows the factors of 649 and the result of 26 to the power of 3 almost immediately. Plus anyone with any maths knowledge whatsoever would know that any even number (or one divisible by 5) can't be prime, so 645 and 372 could be dismissed without even thinking about it.
Plot hole: In the final showdown, when Bond is fighting with Stamper, the girl is wrapped in a chain hanging from a crane and dropped in the sea. After the boat blows to bits, the chain continues to hang down even though there's nothing holding it. It even keeps hanging after Bond's swum down to untie her. What's keeping it there? Do all stealth battleships come with buoyant chains? With both arms at least partially free, why doesn't she just climb back up the chain?
Continuity mistake: The whole big prison bus escape scene revolves around Chris Tucker being handcuffed to the French guy, but when Frenchy's friend arrives in the bus he stands up and hugs him while the handcuff is shown completely unlocked from Tucker's hand. In the next shot and the entire next scene they are still handcuffed together.
Continuity mistake: Toward the end, Carmen Ibanez gets stabbed through the shoulder when she is brought before the big master alien thing. If you were to sustain such an injury, there would be so much swelling, not to mention just destroyed tissue, that you wouldn't be able to move that arm for weeks. Yet a few minutes later, she is seen hefting around a very large assault rifle, and seems to have no difficulty. I guess it's a pretty standard action movie "heroes can temporarily ignore injury in order to save the day" kind of oversight, but it just seems exaggerated in this case, considering how severe the shoulder trauma looked. (01:48:15 - 01:53:40)
Continuity mistake: In the scene where the town folk are having an outdoor festival, Steven Seagal is invited to play with the band. An older gentleman hands him a guitar with nylon string tuners (open headed classical type) but when he takes it from him, it is a Steel string Martin Acoustic (solid headed flat top) guitar.
Plot hole: In the scene where Ashley Judd runs away from her attacker and falls into her aquarium he has moved to the bottom of the stairs - there is no way he would have been able to move that full fish tank. It looked to be about a 30 gallon tank - it would weigh about 400 pounds with the stand and even if he slid it with some superhuman strength, glass tanks are notorious for shattering when you move them full. Plus it would've made enough noise to wake the dead - no way she wouldn't have heard it.