Revealing mistake: During the car chase scene, if you watch the speedometer on the car, it never rises above zero. That, and the obviously poor image quality of the "road" in front of them, shows that they were using projected film in front of the car.
Revealing mistake: When the farmer is going to shoot the sign the bank put up, you can very well see the mark where the hole is going to appear.
Revealing mistake: When the tank/truck driven by Marvin is crossing the stone bridge at the end, they are met by a small German gun vehicle, which they run off of the bridge. The camera angle changes to below the bridge and you see the German vehicle fall from the side of the bridge into the water below. If you look at the bridge material that shatters you can see pieces of wood and hollow areas where obviously it's not real stone. (02:25:00 - 02:30:00)
Revealing mistake: The Union Flag pinned to the back of the taxi driver's jacket is upside down. Since he is part of the government (he's undercover for the Foreign Office) he shouldn't make such an terrible mistake. (01:20:40)