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.
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.
Continuity mistake: Early in the film Bud throws his wedding ring down the latrine and then retrieves it with his right hand so it is covered with the blue disinfectant. In a (much) later scene, Bud has a blue right hand, despite not having had one in the intervening period. (01:44:48)
Visible crew/equipment: During Bud and Coffey's fight in the lab, we see a lightbulb swinging from side to side between the two men. If you look closely, you can see a hand (belonging to a third person) pushing the lightbulb. The only people in the room are Bud and Coffey. (01:44:16)
Visible crew/equipment: Watch the special edition version of the movie. During the scene when the crane is falling down on top of the sub, the camera is following people around the passages. When it comes to the end of a hall, and a hatch is shut in our face, we can see the shadow of the camera equipment in the door. (00:54:13)
Continuity mistake: When Bud is giving his wife CPR and starts to slap and yell at her you see her blink and swallow before they have any life readings. You also catch her closing her mouth as if to wet it when he bends over her body. (02:03:50)
Visible crew/equipment: During the scene where Bud and Lindsey are arguing about who will wear the scuba equipment back to the rig from their downed mini sub, a hand with a cloth wipes water off the camera. It's during the line when the camera is facing Bud and he says "Don't argue with me goddammit, just put it on." This is visible in the 4:3 version for TV, as well as the widescreen version on DVD.
Continuity mistake: When Lindsay is pulled from the pool after she drowns her wet hair is covering her face. In the next shot she is laying on the floor and Bud is smoothing her hair back to give her CPR. The shot changes again and her hair is back covering her face like it was when they pulled her from the water.
Continuity mistake: When Bud sneaks on Coffey in the moon pool, they are seen fighting. During this Bud shirt gets wet and rides up his back. In some shots it goes down again, but then goes right back up.
Continuity mistake: When Bud leaves Jammer behind in the sub, he gives him a strand of rope to keep the two connected. At first Bud keeps the bundle of rope and hands Jammer the loose end, however in later scenes it's shown that Jammer holds the bundle of rope and Bud holds the loose end; as Jammer is feeding him line.
Continuity mistake: When Linds says "I got it. It's headed straight for us," Bud looks out the front window. Watch the umbilical because it doesn't start to move until a split second after the camera is in full frame. (00:54:55)
Other mistake: When the water tentacle enters the rig, in one shot in the 4:3 version of the film on video you can see that the tentacle is a superimposed special effect because of the dead straight line where it is supposed to have come out of the water.
Continuity mistake: When Jammer is alone in the derelict sub and the alien appears, all the electrical devices shut down, as they do in the whole movie. But in the close up shots from the side of Jammer, you can see the light at the top of his helmet is still on.
Continuity mistake: In the under sea duel in the mini subs Coffee smashes the tape player with his elbow, in the next scene, as seen from the outside looking into his sub, you can see it's still intact.
Audio problem: When the crew are running around the passages, a guy with a beard yells something at Bud, and then uses a fire hydrant to put out a small fire. Funny, it doesn't make a noise.
Continuity mistake: When Bud and Lindsay are in the sub after the big chase, water leaks in and Bud searches for something to fix it. He delivers some dialogue while opening (I believe) a first aid kit. The camera angle switches to Lindsay as she says something, and Bud can be seen in the background opening the kit once again. (01:54:44)
Continuity mistake: Bud swims to the moon pool and tries to sneak up on Coffey. Coffey aims a gun at Bud. Bud's right eye is swollen. In the next scene its not, and the following scene it is. (01:43:35)
Plot hole: Granted, Coffee is suffering from "high-pressure nervous syndrome," but if you're a Navy SEAL, wouldn't you notice whether or not your pistol has a magazine in it? Monk pulls the clip out of his jacket and starts knocking rounds out of it for the rig crew's benefit; the same dramatic effect could have been achieved with a handful of cartridges he could let slip through his fingers. You could argue that Monk didn't have enough time to unload the gun and replace the magazine, but in that case, I think the scene where Monk briefly had the gun should have been a bit longer. (Even had the empty magazine been IN the gun, Coffee still might notice the difference in weight, but that would be easier to suspend your disbelief for.) (01:43:53)