Revealing mistake: This actually happens throughout the entire show but is most obvious at the beginning of this episode: When they are in the churchyard it is obviously a studio stage, as there are shadows at all angles around the cast from the studio lights. Also, the lights are quite prominently reflected in Arthur Lowe's glasses.
Factual error: Captain Mainwaring is transferring money from his bank to another branch after it has been bombed. He has the money in a basket and is transporting it on a horse and cart when some of the money starts blowing out of the basket. Pike, Wilson, Walker, and Jones are riding bicycles behind him. They stop to pick up the money and just before Jones tells Pike to ride after Mainwaring to tell him about the money, you can see a silver car parked on the left hand grass verge in the direction Mainwaring is heading. This car was obviously made long after World War Two finished.
Character mistake: When Mainwaring and the others are discussing how to break the news to Godfrey about his cottage, it is mentioned that the roof is made of thatch. However when Mainwaring, Wilson and Pike go to visit Godfrey, the roof of his cottage can be seen and it is slate, with no thatch anywhere in sight.