Other mistake: In the scene where the U.S.S. Oklahoma capsizes, she clearly rolls to the port side. When the bow comes into the air, one can see a hole on the starboard side; obviously from a torpedo. This cannot be. The starboard side was facing the U.S.S. Maryland and thus protected from arial torpedoes. That hole should not be there.
Other mistake: Look a bit more closely at the scene in which the USS Oklahoma capsizes, as sailors are falling from the deck, etc. Despite the huge amount of dollars spent the battleship is very out of scale, especially the 14" main battery guns, which look suddenly like props in a high school play. Similar "cheap prop" shots abound in the film.
Other mistake: When the first torpedo hits the American ship (killing the two guys hanging on the side) Danny and Rafe jump up from the car. Their cue to do so is somebody (possibly the Director) shouting 'Boom.', which is still audible on the finished film soundtrack. (01:24:25)
Other mistake: During take off from the carrier, 600 miles at sea, trees and a shoreline are in the distance.