Revealing mistake: When the platoon hear the church bells, they mistake it for the invasion signal and construct a barricade across the high street. If you look behind them you can see cars parked on the road in the distance that date from well after the 1940s.
Visible crew/equipment: When Mr. Mainwaring, Mr. Wilson and Pike have left the radio shop and they are walking up the street, you can see the crew in the reflection of the shop windows.
Visible crew/equipment: At the end of the film when Mainwaring is walking to the bank, you can see the camera lights in the window of Fraser's Funeral Parlour.
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.
Visible crew/equipment: When the platoon are marching past and their uniforms appear on them, there is a large camera-shaped shadow on the road.
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.