The action mostly takes place during March. After Hannay is rescued from the location of the musical event, David takes him to a ruined castle where they change clothes. It is seen to be either near sunset or sunrise, but in March sunset would take place around 6pm, and surely a musical evening event would therefore take place when it was already dark. The question is why would they wait until the next morning to go to the castle, especially as they went afterwards to David's home - in daylight. Where did they spend the night, and why didn't they go to David's home immediately?
Appleton's beard appears and disappears.
When Hannay and Scudder are talking in Hannay's flat, the drink in Hannay's left hand disappears and reappears between camera angles.
When members of the Admiralty are being spoken to, one of them has medal ribbons for medals issued at the end of WWI, namely the Victory and War medals. This film is set before WWI.
At the health resort where Hannay is drugged by the Prussian agents, a concert is taking place. As the guests assemble, we see a poster advertising the concert, which gives the date as Wednesday, 13 March 1914. 13 March that year was a Friday.
The newspaper in which Scudder learns of the murder of Lord Harkness is dated Saturday, March 4, 1914. March 4 that year was a Wednesday.
The rounds Hannay removes from Scudder's gun are clearly inert as the cartridge cases have dented or absent primers indicating they're recycled from previously live ammunition.
Whilst in Scotland, as a guest at the ancestral home and on the heaths, Hannay, wears Cherry Red Dr Marten Airwear boots (first invented in 1960). These are first seen under a chair whilst he is changing in the bedroom.
The train in which Hannay travels to Scotland is far too modern. The coaches were built by the LMS railway company which was formed in 1924 and the loco was built after WW2.
As Hannay looks out the train window as Police Board the train, a "First Class" symbol appears on the window. This is in the BR "Totem" style, which did not appear until 1948 when the UK Railways were nationalized.
Robert Powell's hair (perm) is not a hairstyle of the time (1914) and is the fashion of the time the film was made (1978).
When the police and Hannay search Appleton's house, they find a dummy head with false hair, beard and moustache for Appleton to impersonate Sir Walter. Appleton had already left to go to Westminster to carry out his plan, but how could he without these vital items?
When it is established that there is an explosive device trigger in the Westminster clock tower, the obvious course of action would surely be to evacuate the Houses of Parliament? However, this is never suggested.