When Hannay and Pamela are in the hotel room, he dries her stockings by placing them under two china ornaments on a shelf over the fireplace. Later, when she removes her stockings from the shelf, the two china ornaments are now spaced much further apart, with another ornament in between them.
Hannay gets the train from London to Scotland, but the train on that journey is seen bursting out of Box Tunnel near Bath, which is nowhere near the line from London to Scotland. The locomotive changes from a London and North-Eastern one, with a prominent sign "Flying Scotsman" above the smoke-box door, to a Great Western one, with no "Flying Scotsman" sign.
Near the beginning of the film in the scene with the Memory Man entertaining the audience by answering their questions a woman yells out, "Who is the last British Heavyweight champion of the world?". Beside her is a man who mouths the woman's words in synch with her.