Continuity: When the SEALS take over, they lock up the crew. After closing the door on Ed Harris and the shouting Mary Elizabeth Mastrantonio, one of the SEALS hangs a hat over the spyhole. The next time we see the door, the spyhole isn't covered.

Revealing: 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. (Time)

Other: When Ed Harris is dropping down the Abyss there are a couple of time that bubbles come out of his mouth or can be seen in his nostrils, even though he is supposed to have been breathing liquid for quite some time. (Time)

Continuity: When Ed Harris gets used to the Liquid Breathing Suit you can see air still in his helmet after he goes in the water. That shouldn't be! The purpose of the suit is to get any remaining air out for it to work. (Time)

Factual error: There are no fish in the entire movie except the scene in the sub with the crabs on the dead guy. You'd think there would be fish in the ocean at least every now and then.