When Jim returns one morning from looking for Baxter's murderer, he finds Nancy asleep. The amount of the rug covering Nancy changes between when he kisses her and when she wakes.
When Olaf comes out of the house and sees Jim talking to Madge, the background changes between the wide shot of the three of them and the close-up of Olaf getting the axe.
When Sturak stands after talking with Dr Gelster at his house, his tie is hanging out from his coat. An instant later when he is walking past the window, the tie is tucked in.
Jim states that the USS Arizona "is still carried on Navy lists as a fighting ship of the line." The Arizona was actually officially struck from the Navy Vessel Register in December 1942.
After Jim and Mal finish their visit to USS Arizona wreck, a battleship is shown steaming at sea, ostensibly the USS Arizona. Actually, the battleship shown is the USS New York, which was two classes older than the USS Arizona and its sister ship USS Pennsylvania.
When the plane taking McLain to another island begins taxiing, the door is still partly open.
Early in the film, when they're flying into the Hawaiian Islands, the stewardess points out Molokai Island "on the left" and Oahu "on the right", but the views out the windows show the opposite. Otherwise, the plane would have to be flying backward.
Just before McLain gets on the plane to go to the leper colony, the audio and video of his lines are out of sync.
When Jim and Madge are walking through a hotel lobby, a moving shadow of the boom microphone can be seen on the wall behind them in two shots.