Character mistake: The Professor refers to his pistol as a "revolver" but it is a semi-auto.
Factual error: Hannay travels to Scotland on The Flying Scotsman which ran from London to Edinburgh, The Forth Road Bridge is actually 12km further West of the Port of Edinburgh, so Hannay couldn't jump off the Flying Scotsman onto the Forth Bridge.
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.
Other mistake: When we see the Church Hymnary being opened, the date on the left-hand page is signed by Margaret in 1928, but the book is dated 1932.
Revealing mistake: When the compere introduces Mr. Memory in the Music Hall at the start of the film, Robert Donat's stand-in is sitting in his place in the audience on at least two occasions.
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?