Factual error: [Special Edition] The Statue of Liberty is incorrectly shown to be facing the Narrows bridge.
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: 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.