Factual error: In the opening scenes by the farmhouse, the fields in the distance have "tramlines" - used for accuracy when crop spraying. The scene is set in 1941 however tramlines didn't come into use until the 1950s. (00:02:20)
Factual error: When the real German soldiers are playing 20 questions in the bar, one of the cards shows the name of Genghis Khan. This is an English-language word; as Germans, they would have written Dschingis Khan instead. As the whole scene deals with exposing the British/American spies and subtle differences in their language or behaviour, this is especially unfavorable here.
Factual error: Near the end, when Lt. Raine is being interrogated by Col. Landa, there is a phone on the table with a coiled phone cord. Coiled phone cords were not used until the late 1950s.
Factual error: During his briefing for Operation Kino, Lt. Hicox quips "Paris when it sizzles", which was not a thing in WWII; it is the title of a 1964 film, itself taken from the 1953 Cole Porter song "I Love Paris."
Factual error: During the baseball bat beating scene, the "hitter" says something about Teddy Ballgame going yard. "Going yard" is more like a 1990s term, not one used way back in 1941.
Factual error: In the opening credits for "Stolz der Nation," Joseph Goebbels' name is spelled "Goebbles." This is easily visible both in the actual film and in the "Stolz der Nation" bonus film on the DVD.
Factual error: When we first see him in Royal Marines uniform, Hicox is wearing a beret with a short 'tail' (the end of the drawstring used to tighten the beret). This is indeed a feature of military berets in some countries, but not in Britain.
Factual error: At the start of Chapter 3 the title reads "1944 Shoshanna Dreyfus four years after the massacre of her family." Chapter 1 takes place in 1941. So it is actually three years.
Factual error: When Colonel Landa offers to surrender in exchange for not warning Hitler he is about to burned alive in the Paris cinema he points to a telephone with a rotary dial with alpha-numeric characters. I believe that was a feature of North American telephones after WWII.
Factual error: After carving the swastika on the Nazi private's head that they let go, Donny tells Aldo that he's getting good at that. Aldo then proceeds to make the joke about getting to Carnegie Hall and practice. This has been a well known and common joke for years, however the earliest known written instance of this joke is from 1950. Plus the joke originates in New York and Aldo is from Tennessee, saying he's from the Smoky Mountains. So him referencing this joke in such a manner does not match the time frame at all and is way out of place.
Chosen answer: It is explained shortly afterwards that a real German would hold up his thumb, index and middle fingers to indicate three. Since, the major already suspects the Captain of being a spy, holding up his index, middle and ring fingers to indicate three confirms this.
Xofer