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.
Revealing mistake: When the crane falls down in front of the rig and then over the cliff into the abyss it's as if the rig was already just a few yards away from the abyss but when the umbilical pulls the rig again (after Bud says to grab onto something) suddenly there's enough space for the rig to be dragged at least a few hundred yards as if the rig never moved from its touchdown position earlier in the film.
Revealing mistake: When Bud is unscrewing the trigger from the nuke down at the bottom of the abyss, there are no threads on the mechanism to require unscrewing. The part of the device that would have the threads is plainly visible.
Plot hole: Water pressure seems to be very picky in this film. It crushes Little Geek after passing 17,000 feet but somehow manages to leave Big Geek intact. Also if Big Geek could fall that amount of distance before imploding then why did Flatbed implode after only falling a few feet?
Revealing mistake: When he's on his way to send the nuke down the abyss, Coffee leaves the other SEALs to guard the rig's crew in the kitchen. He goes through a door, locks it and secures it with his belt, and then bangs on it to test its security. It moves more than a metal door in a metal housing would. (01:37:43)
Factual error: When Bud is dropped onto the spacecraft floor by the alien who rescued him, air trapped in his suit comes off in large bubbles. At 18,000 feet bubbles would be compressed so far that they would be BB size. Also, with all the movement Bud experienced on the way down, no air could possibly have remained trapped in the folds of his suit.
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.
Factual error: During the flooding of the drill rig, Bud's wedding ring saves the day by preventing the barrier door from closing. Even titanium couldn't stop a moving hydraulic barrier, in ring form. It's very hard in terms of resisting scratches, but that doesn't mean it wouldn't deform or crack.
Factual error: When disarming the nuke Bud is trying to figure out which one of the two wires to cut. With only two wires running between two separated modules (in the film, one part is unscrewed from the other) any current flowing through one wire must be returned through the other in order to conserved electric charge. Cutting either wire, in this case, will result in breaking the circuit. There is no way for either side of the circuit to detect which wire(s) were cut.
Plot hole: Why wasn't the umbilical to the "Explorer" unhooked from the rig after the rig was set down? Everyone knew things were going to get rough with the hurricane coming, so the umbilical should have been taken care of before the hurricane became a factor.
Plot hole: Coffey uses the submersible "Big Geek" to carry the armed nuclear bomb to the NTIs. If Coffey was that desperate to blow up the aliens, he could have much more easily set the timer for 30 minutes, driven one of the submersibles far out over the abyss past the drop-off, and simply dropped the bomb down and let it sink under it's own weight.
Continuity mistake: When the crane breaks off and falls into the water, it JUST misses the rig by a few feet (very visible when they're looking out of the window). Then the crane falls off of the edge and starts to pull the rig. The rig is pulled much farther than the previously shown distance to the edge.