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.
When in the US the newspaper is dated August 21st 1940. This should be 1941.
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.
When Eva calls the "home office" in New York, the phone has the distinct British "ring-ring-pause-ring-ring-pause" pattern. It should be the US "ring-pause-ring-pause" pattern since the office is located in New York.
The name of the hotel in Las Cruces is spelled wrong. It should be Alamogordo Inn, not Alamagordo.
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.
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 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.
When Eva recites some of the names of US states and their capitals, she includes Hawaii and Honolulu. Since Hawaii did not become a state until 1959, there would have been no reason to include it in her list.
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.
The US flag seen briefly when Eva and Romer come to America is the current 50-star flag, which came into use in 1959 after Alaska and Hawaii became states, long after World War II.
The aqua colored convertible Eva drives in New Mexico, 1941 is actually a 1946-1948 Chevrolet Fleetmaster.
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.
As Eve approaches the railroad tracks when she flees to Canada on foot, the rising sun is in the background. Since she is entering the scene from the left, that means she was heading south, not north, to reach Quebec.
Young Eva (Hayley Atwell) has dark brown eyes. Old Eva/Sally Gilmartin (Charlott Rampling) has green eyes.