In the "flat feet" scene, Milligan takes off his left sock twice.
When the Milligans are in the air raid shelter Spike (playing his own father) goes to pour some wine but stops before any wine is poured, but in the next shot all the glasses are filled with wine.
When the lorry the men are in is diving across the field to the crashed German bomber, you can clearly see the lorry tracks on the grass made by a previous take.
When Spike plays the trumpet near the end of the film, after the pillow fight, the feathers in the end of the trumpet horn do not move. If he were, in fact, blowing through the trumpet, these feathers would blows about.
The red and blue teams are driving Willys MB Jeeps in 1940. The Willys MB was not manufactured until 1941 and was not used by the British Army until 1942.
In the dance hall, when they start to sing the national anthem after the director's announcement, the third girl from the front clearly mouths "Queen" while the soundtrack (and historical accuracy) provide "King".
When the platoon are in the field about to start the 5 mile run, as the camera moves around behind the Sgt, several crew members (and boxes of equipment) are briefly visible standing at the front of the lorry.