Deliberate mistake: As the sub rises backwards to the surface, the stern emerges from the water at a steep angle, then rises near-vertically so that the boat is virtually standing on the tip of its bow. Anything left loose on a countertop would surely fall off. But when the boat falls onto its belly, a close-up shows a pistol sliding off a sink counter into the hand of the Captain- because it's dramatic and cool looking, yet extremely improbable- especially considering that an open tin of shaving foam, its lid and a foam brush all lay on the same counter, undisturbed.
Factual error: In the close up shot showing the record on the record player, the label correctly identifies the song that played as Benny Goodman's "Sing Sing Sing (With a Swing)" but the label also states it is a "Swing Classic," a classification only used when the record was later reissued. The label is inappropriate for a World War II time frame.
Continuity mistake: When Claire is in the Captain's quarters, the locker falls open. As the camera pans up and left across the inside of the door, it slowly passes a photo of Cmdr. Winters in front of a banner that partially reads 'Welcomes Sinatra', and to our left is Frank Sinatra partly shown in the photo. Moments later, Olivia is looking at that same specific photo, and in close-up you can no longer tell who's at the left side (obscured by a hanging jacket) and the banner now reads 'Welcomes Goodman'. (Apparently there was a 'rights' issue that arose during filming that forced a switch to Goodman's name and music, and the earlier Sinatra shot was used in error.)
Continuity mistake: When Claire enters the Captain's quarters, she glances in to see the white desk is very well lit, and his Patrol Log is placed on top. To the left of the log is a brown cup and there is nothing between the log and cup. Seconds later, when she is looking down on the desk, the lighting is extremely dim, and a pen has appeared between the log and cup. The log is also in a different position (further away from anyone that sits at the desk) and Claire has to pull it closer to get it to the spot that it was at when first seen.