Factual error: In the aerial shot over rural Britain near the beginning of the movie, there are two modern cars visible. Too new to be early 40's models.
Factual error: When we are in the Colonel's office at the US army base there is a US flag in the corner. It has 50 stars on it, as you can tell by the pattern. There were only 48 stars on the flag during WWII.
Factual error: When Michael Caine is standing outside the village church, it is clearly visible that double yellow line road markings have been blacked out (covered up). The film is set during the war, but double yellow lines did not make an appearance in the UK until 1958, therefore it is clear that the filmakers blacked them out to avoid an anachronism.