Factual error: The carriages on Hannay's train feature British Rail 'class' totems on the windows. These didn't appear until the 1950s, yet it is supposedly 1914.
Other mistake: After David Warner kills a man with his long thin sword, he pulls the sword out and puts it back in its scabbard, but there's no blood on the sword or anywhere.
Other mistake: This takes place in 1914. While the Prussian agents drive away with Hannay, after kidnapping him from police custody, on the road you can see a modern marker for a car parking space, near the corner. (00:25:10)
Continuity mistake: As the Prussian agents escape by carriage with Hannay after 'springing' him from police custody, you can see modern markings on the road for a car parking space.
Revealing mistake: Towards the beginning of the film, when Hannay has been arrested for the murder of Scudder he is being interviewed by Chief Superintendent Lomas. Hannay removed the bullets from Scudder's pistol whilst he was staying in his apartment, and Lomas is shown putting them on the table. One of the bullet casings has a hole drilled through the center of it, a typical method used to identify inert rounds as being safe to handle.
Factual error: Towards the end of the film Hannay and Chief Superintendent Lomas are interviewing two senior naval officers about the fake Sir Walter Bullivant's activities. One of the officers is wearing medal ribbons including the British War Medal and the Victory Medal. These were instituted in 1919 for serving in the Great War, but the film ends in May 1914, about 3 months before the war had even begun.