Revealing mistake: When one of the bad guys is being dragged around by the monsters and thrown against pipes and walls and such, in wide shots you can see there is no monster really pulling him, and from the stiffness and position of his body, he is likely on some sort of device to swing him around.
Revealing mistake: Occasionally, when the characters are being eaten by the sea-monsters, you can see pieces of the computer-generated beasts going "through" the victim.
Continuity mistake: When the guy and the girl (the stars of the movie) are jumping out of the big boat, you can clearly see that when they land in the water they are going to fall off and they cut it so that it looks like they landed great.
Continuity mistake: When they have first transferred to the cruise liner, one guy is using a welder on something. In one scene the welder is lit, and in the next one it is not.
Deliberate mistake: At one point during the big escape chase scene, Finnegan takes a turn and the jet-ski he and Trillian are on side-swipes a wall and it's clear that they're about to fall off. The film cuts away briefly and then we see them and they're zooming along again as though nothing happened. The scene is portrayed in real-time so there's no way they had time to spill, get back up again and build up enough speed in the time between edits. Slightly sloppy editing. (And this is not referring to the other moment in another mistake where the same thing happens when they exit the boat. It actually happens twice during the scene - that moment and this one).
Continuity mistake: When the woman is "sucked" into the floor of the bathroom, at one point she accidentally pulls a faucet from a sink next to her, causing water to begin spraying upwards and raining down. Problem is, less than two seconds later, she's already completely soaked and we see a closeup shot of her kicking her feet, and there's already a large volume of water on the floor. Far too much water for how short a period of time it's been coming out of the faucet.
Visible crew/equipment: Near the end of the owner's speech near the start, there is a brief circling shot with a boom operator sitting on the railing behind him.