When Almasy returns to the cave, he is wearing a German Wehrmacht issue tunic. From a distance, his outfit looks like German Army. However, looking closer, it is completely without insignia (other than plain privates's shoulder insignia). Makes perfect sense that the German Army would most likely not give him a piece of regulation uniform. If this is intentional, it shows perfect sense for detail. See more...
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Continuity: In the scene where Willem Dafoe is conversing with another male British agent as the German paratroopers invade, a British female worker passes him as he is about to go down the flight of stairs. As he reaches the ground floor, she passes by him again as she goes up the same stairs he just came down - seemingly far too quick to be possible.
Continuity: In the scene where Almacy is trying to dig out the workers from the car in the sand dune, the camera switches back and forth between Almacy and Katherine as they talk. Each time the camera shows Almacy, the long white scarf around his neck is wrapped or dangling in a different way, and missing entirely at the end, as if they were tired of messing with it.
Factual error: In the interrogation scene with Carravaggio, the German officer is addressed by the private Wehrmacht soldier as "Herr major". The officer is SS. By his shoulder patches he indeed has the equivalent rank of a major, but the correct SS rank is "Sturmbannführer". SS officers were never addressed as "Herr", but simply with the rank.
Plot hole: It's unusual for Juliette Binoche's nurse to have a beautiful blue dress on when she retires with "her" patient to the abandoned monastery. Maybe it was an artistic homage by the film's director to her marvelous leading role in the movie, "Blue." However, given the unstable situation in post-war Italy, shouldn't she still be wearing her British khaki Army uniform?