Other mistake: Recreated newsreel of a trip to Japan by Moe Berg before Pearl Harbor attack shows copyright date of MCMXLIV (1944) in the lower left corner, 3 years after the attack. (00:16:25)
Factual error: During the plane ride into France, the Paratroopers are holding/carrying their weapons by their sides. In reality, their weapons (M1 Garands, B.A.R.s, etc.) would be carried in special "bags" strapped to their parachute harness. This not only protected their weapons, but also secured them to their person.
Continuity mistake: In the first WW2 flashback the protagonist is handing the various items to the Nazi doorman. When he puts down the pen, he is doing it with a left hand in the table close-up, but he picked it with his right, as the left arm is busy holding the coat. (00:02:05)