Stupidity: Monk steals the magazine from Coffey's SIG. However, I don't see how he could have jacked the slide to eject the round in the chamber without being noticed. Someone as paranoid as Coffey was at this point would not have left the chamber empty. (Just FYI, when you load an automatic pistol with a magazine, you have to pull back and release the slide to load the first bullet in the barrel.)
Other mistake: At the end of the film the NTI's entire ship ascends from the abyss to the surface. What happened to the rest of the sea floor that Bud, Lindsay, and Coffey had to race over during their battle? All of that seems to disappear when the mothership comes up.
Factual error: There are no fish in the entire movie except the scene in the sub with the crabs on the dead guy. Phytoplankton are attracted to artificial lights which means a whole food chain develops around submarine structures like the Deepcore rig - just look at any film of the shoals of fish feeding around the legs of an oil rig. You'd think there would be fish in the ocean at least every now and then, but we don't see a single one.