Early on when Eva is in training she recites all the American states and their capital cities. Hawaii is included even though it wasn't a state in 1939.
When Eva and Lucas first go to New York, the scene is set by an American flag hanging from the corner of a building. Unfortunately, it is a 50-star flag, which did not come into use until Hawaii was admitted as the 50th state in 1960.
The aqua colored convertible Eva drives in New Mexico, 1941 is actually a 1946-1948 Chevrolet Fleetmaster.
The motor vehicles depicted in 1940s New York feature long European style license plates. American license plates have always been much shorter than European ones.
The notice of Romer's memorial service shows his awards as KCB, MC and Bar, Croix de Guerre. The order of precedence is strict, and the awards should have been in the order OM (Order of Merit), KCB (Knight Commander, the Most Honourable Order of the Bath), Military Cross and Bar, Croix de Guerre.
When in the US the newspaper is dated August 21st 1940. This should be 1941.
When Eva is crossing the border from New York state into Quebec, on the west side of Lake Champlain, we see a majestic mountain range on her left, or west, side. There is no such mountain range anywhere nearby, much less between Champlain and the St. Lawrence river.
When Eva is being tailed in town (as part of her training), she walks towards the rear of a parked car (registration BPT591). In the next shot she is walking towards the front of that same car.
One scene set in wartime London shows a motorcycle being ridden by a soldier. The number plate on that motorcycle shows the year indicator letter C. This means the motorcycle was registered in 1965.
Young Eva (Hayley Atwell) has dark brown eyes. Old Eva/Sally Gilmartin (Charlott Rampling) has green eyes.
The 1940's Marines have the rank insignia adopted for the lower ranks in 1958-1959; they have a "rocker" on the bottom.