Continuity mistake: When we first see Jones's van, it already has the flaps for the gun ports in the side, even though the van isn't converted to an armoured vehicle until later in the film.
Continuity mistake: When Capt. Mainwaring is demonstrating making petrol bombs Godfrey is wearing a beige waistcoat, but in other shots of the same scene he isn't. (00:37:52)
Continuity mistake: When Captain Mainwaring and Corporal Jones enter the camp site in the steamroller, they run over a few tents and squash all bar the last one flat. When the steamroller is trying to turn round, all the tents that were previously squashed are now standing up again.