Whilst Kate & Andrea talk at a table, one of two candles alternates between burning and extinguished depending upon camera angle.
In the opening scene an aging Lee Miller pours a glass with gin. Minutes later as she talks with a visitor she raises the glass and the level of liquor is suddenly higher.
Arinze Kene who plays Major Jonesy is an African American in charge of white troops in 1944. African American soldiers did not see combat until later that year and African American officers would not have been in charge of white troops until after the desegregation of the armed forces in 1948.
Miller is refused entry to Hitler's apartment because it's "Officers Only." War correspondents were accorded the Captain rank, so, technically, the US Army guard should have granted her admission.
The car that Lee gets into for transport to the air base to deploy to Europe does not have headlight masks, which were necessary on all motor vehicles in the UK during WW2.
When Lee and David are at the concentration camp they witness the opening of a train cattle car. David (Andy Samberg) goes to take a picture and he removes his glasses. In the next shot from a different angle he is wearing the glasses again. Two seconds later he is no longer wearing them.