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 addresses Pamela by name in the taxi carrying them (purportedly) to a police station. But how does he know it? They only previously met in the train and the assembly hall, and her name wasn't mentioned in either scene.
The "commercial traveler" played by Gus McNaughton who reads the newspaper article aloud on the train describes the woman who discovered the body as "charwoman Elizabeth Riggs," but when we see the article in closeup a moment later, that sentence states simply that "a cleaner" discovered the body.
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.
I question the doubt cast on the pronunciation of Alt-na-Shellach. Wikipedia says the place is now called Achnashellach and derives from Gaelic Achadh nan Seileach. The initial "Seill" is undoubtedly pronounced like Shell-.
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.