During the car/motorcycle chase on the mountain road, the painted road surface markings disappear several times, mostly during wide shots.
In the wide shots, the engine of the passenger train with which Peter Cunningham tries to escape, has large smoke deflector plates. When stopped in the station near Meursault, however, the engine has no more deflector plates.
When Stanislas and Antoine enter Mersault and are standing in the place across from the Hotel du Globe, a modern lit up sign for the hotel stands above the doorway. In World War II, no lights were permitted outside that could be viewed from the air so if the sign had been there, it would have been dark.
The RAF bomber Terry-Thomas and crew are flying is mostly a B-17 Flying Fortress. This is highly unlikely, as the RAF mainly flew Lancasters, Halifaxes and, earlier on, Stirlings.
Obvious use of chroma key compositing in the parachuting scenes.
The whole story speaks about 3 crew members.
When jumping out of the crashing plane, you can see 5 members.
At the very beginning, we see an aerial shot of Paris; however we can clearly see modern buildings built in the 60s.
Painted road markings weren't introduced in France until post-WW2 (and the movie takes place in 1941).