When Stingo goes from the entry hall of Lesley's apartment, she asks him what he wants to drink, and immediately he has a drink in his hand. Also, while they are in the inner room, Stingo has his jacket on, and then instantly has his jacket off.
There was no Jewish ghetto in Cracow in 1938. Ghetto was established under German occupation in March 1941.
Slavic surnames ending in -ski/-skiy are, in Slavic grammar, considered adjectives, and so the female form is -ska. Sophie's and Eva's surname should, therefore, be Zawistowska. Moreover, it is unlikely for Eva's name to be spelled with a 'v', as the proper Polish form is 'Ewa'. ('v' does not appear in the Polish alphabet and is only used in foreign names and loanwords.)
The sirens and "Bunny Ears" affixed to the late-1940s vintage NYPD cars were incorrect. NYPD cars of that era were equipped with only a rectangular illuminated sign reading "POLICE", made by the Julian McDermott Corp of Queens, NY. The Federal "Pulsator" sirens affixed to the movie cars were not manufactured until 1963 and only appeared on NYPD cars in 1964.
When Sophie is recounting the languages she knows, she includes "Hungarian," but the correct term is "Magyar," as any Pole would know.
(at around 3 mins) When Stingo is moving in, he is carrying 3 cases of Spam on his shoulder. They barely move despite him writhing around to get the door open. When he gets into the room, he drops them on the bed, and it can be seen that most of the cans are glued to the cardboard. The actor even flips the top row over on the bed, and they stay attached.
(at around 1h 38 mins) When Rudolf Hoess is at his desk and his head is starting to hurt him, the smoke from the crematoria in the background is noticeably not moving, revealing it's a painted backdrop.
When Nathan toasts Stingo on the bridge, as the shot pulls back, several cars from 1982 are seen. This was obviously an issue with how long they could hold up the bridge traffic; they needed to hold it up an extra minute or maybe lacked the budget to pay for late-1940s cars to drive by instead. Also seen are the lights of The River Cafe, a waterfront restaurant under the bridge that didn't open until 1977.
At around 1h45m, when Rudolf Hoess is washing up in front of a sink, a crew member is visible in the mirror on the right side.
Sophie misidentifies the rank of Commandant Rudolf Hoess as Reichsführer which was Heinrich Himmler's rank at the time. The correct rank for H?ss was SS-Obersturmbannführer.
When Nathan and Sophie drink what Nathan calls a Chateau Margaux, the color of the wine in the glasses looks nothing like a Bordeaux, let alone a Margaux. It looks like a cheap rosé wine or a very badly made red.
Nathan arrives at the park carrying some boxes for Sophie and Stingo as presents. Sophie takes out from the second one a pair of shoes that supposedly are new. It can be seen by the soles that they have already been worn.
During the "Choice" scene, Sophie refers to the officer as "Hauptmann". The SS had different rank designations, separate from the Wehrmacht. The correct rank designation would be "Hauptsturmfuehrer", evident by his collar tab. This title is, however, equivalent to "Hauptmann" (Captain) in the Wehrmacht Heer.