Continuity mistake: Hannay is talking to the milkman inside the door. Outside the door you can see across the street, the two guys walking down the sidewalk. A moment later, Hannay goes toward the door and now there's the milk wagon on the street right in front of the door. When Hannay pointed out the two guys across the street to the milkman, the milk wagon wasn't there and the milkman is inside with Hannay so he couldn't have pulled it up.
Continuity mistake: In the apartment when Hannay discovers the dead women the telephone changes from white to green.
Suggested correction: The film is in black and white. How can you tell what color the phone is? We're you watching a colorized version? Or did you mean to post this on one of the remakes?
Continuity mistake: When Pamela takes off her stockings in the hotel room, Hannay dries them by placing them under two china ornaments over the fireplace. When Pamela removes the stockings from the shelf a little later on, the ornaments are now much further apart, with another ornament placed between them.
Continuity mistake: When Hannay and Pamela are hiding under the waterfall to escape the police, in a long shot Hannay's free hand is against the rock behind him, but in a close-up, the hand is in his pocket.
Continuity mistake: When Hannay and Pamela are on the bed at the inn, Hannay asks Pamela to pass a nail file to him and you can see Hannay is about to take a bite of his sandwich. In the next shot, his hand with the sandwich is well away from his mouth.
Continuity mistake: When Professor Jordan is speaking to Hannay, he draws out a revolver with his left hand, but when the Professor's wife leaves the room, we cut back to the Professor, and he now has the revolver in his right hand.