During the shelling of the French town, smoke from the explosions goes behind the matte painting of the tops of the background buildings, leaving them apparently suspended in mid-air.
Just before she goes on stage to play for the German infiltrators, Dora Bryan has her piano accordion on upside down. In the next shot, on stage, she has it the right way up.
During the German offensive in France 1940, there is a Jeep with a civilian registration, EAY891. The Jeep wasn't invented until 1941. And a military vehicle wouldn't have had a registration number in this range, if it had one at all.
The film is supposedly set in 1941. When Sid is trying to compose a lyric for Lili Marlene a photo of a footballer is shown attached to the wall. This footballer played for that particular club in the late 50s and early 60s so he could not be playing at the time of the war.