Audio problem: Jonesy is playing the organ. A pigeon 'flies' out the top of the organ and lands on the keys, so Jonesy picks it up and moves it, taking both his hands off the keys. Yet the music plays on.
Continuity mistake: When the second bottle thrown by Pike lands on the floor, the glass from the first bottle has all disappeared.
The King Was in His Counting House - S5-E7
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.
Revealing mistake: When the knight moves back and forth during the clock mechanism's operation, as he swings his sword, a blue pullover sleeve is visible beneath his armour, revealing that he is an actor in costume and not an automaton.
Revealing mistake: The lights in the café are not working, despite the room being brightly-lit from above (i.e. the brightness cannot be attributed to sunlight entering through the window).
Answer: The show is a comedy, this was played for comedic effect and to show that in times of extreme fear, in this case about to be crushed by a steam train, the men had an adrenaline surge strong enough to pedal fast enough.