In the opening scene when the German U-boat is preparing to torpedo the warship, the view through the periscope has the ship moving left to right. When the torpedo strikes, the ship is moving from right to left. The torpedo explosion is on the near (port side) rather than the far (starboard) where it would have struck in the original scene.
When Bill returns to his office from the lab, he is shown opening the door twice between shots from outside and inside the office.
The ship that's torpedoed in the opening scene is seen twice. It not only reverses direction between the two shots, it's not even the same ship. The configurations are noticeably different.
During the struggle with the policeman at the Sufferagette march, Rosalind Russell knocks the cop's hat off. Switch to William Powell recovering from being pushed away and rushing to help. Switch back to Russell and the cop, whose hat is back on his head.
Lt. Gordon's comments on the frequency analysis are totally wrong. 'E' is the most common letter in English, but an enciphered message is not English any more. In general, the most common letter in the enciphered message *stands for* 'E'. Similarly for his comments on Spanish, 'Q', and 'U'. However, the lack of a 'Q' might actually indicate it could be German if there is no 'Q' in the German alphabet and the originating and destination alphabets are the same.
Near the end of the movie, in madam Kerloff's room at the Park Hotel, Gordon sees the note from the messenger and asks the messenger to take him to the sender of the note. When Gordon gets in the elevator he says "down", as if he knew where the message came from. He should have let the messenger tell the elevator operator which floor to go to.
This movie takes place during World War I. The map of France on Lt. Gordon's office wall includes Alsace and Lorraine, which weren't returned to France until after the war.
Though set in 1917, except for a few scenes of uniformed soldiers, everyone is wearing 1930s clothing.
Lt. Gordon, after his first all-nighter at the bureau, looks at his wristwatch to see the time. Men didn't wear wristwatches in 1917; they were introduced after the war when French airmen made them fashionable.
Late in the picture, there's a bit of ADR where Powell's voice is overdubbed by someone who doesn't sound remotely like him. The dubbing is done only when Nieterstein's name is used and other characters speak of him, too. Evidently Romero's character's name was changed after filming took place.