Factual error: The lake that Jack told Rose he went ice fishing on when she was threatening to jump is Lake Wissota, a man-made lake in Wisconsin near Chippewa Falls (where Jack grew up). The lake was only filled with water in 1918 when a power company built a dam on the Chippewa River, six years after the Titanic sank. (00:39:05)
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.
Continuity mistake: Just before Demi Moore is about to get her head shaved she sees the base commander about equal treatment, and we notice very visibly that O'Neil has one side of her face bruised and all red and swollen. But in the next scene, which takes place moments later, when O'Neil is shaving her head, her injuries are all gone. Where did they all go to?
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.
Continuity mistake: In one of the scenes Hopkins is trying to make what I think is a fish hook or something. He's obviously been in the wilderness for a while so he's not clean shaven but he isn't exactly beardy either. However, during the scene with this fish hook his beard changes from moderate to bushy to moderate again within seconds.
Visible crew/equipment: Early in the movie, Melvin walks for the first time to the restaurant in which Carol works. As Melvin turns the corner on the sidewalk and walks towards the camera, he is surrounded by extras playing people he must dodge. If you look in the center and right background, you will see New York spectators standing in the middle of the street, watching the movie being made. (00:10:20)
Continuity mistake: After Nick becomes a hero, he wears a cast on his right arm. However, when he and Kate go to dinner with Kate's boss, Nick's cast mysteriously disappears for one shot. They are sitting at the table at the beginning of the dinner and Nick picks up a glass with his right hand, with no cast. The next time you see Nick, he has a cast on his right arm again.