The Dirty Dozen (1967)

Factual error: During the war games they have Jefferson pose as a major in order to facilitate the commandeering of the ambulance and the jeep. Regardless of their personal feelings in the matter the ambulance crew and the driver and troops in the jeep would be perfectly aware that no black man would ever be promoted to a position of authority in an otherwise all white command. We may find it repugnant today but the US Army was rigidly segregated during World War 2 - and it stayed that way until 1948. Jefferson may have been inducted into a special unit like the Dirty Dozen but considering that the future of the entire mission is riding on their success at the games, throwing it all away like that makes no sense at all.

Col. Everett Dasher Breed: Reisman! Some people may consider you a first-class officer. But as far as I'm concerned, you're a disorganized, undisciplined clown. I'm gonna' make it my business to run you out of this Army.
Major John Reisman: I owe you an apology, colonel. I always thought that you were a cold, unimaginative, tight-lipped officer. But you're really quite emotional, aren't you?

Trivia: Not really a mistake, given the need for drama in a war film, but the mission takes place the evening before D-Day, meaning the Allies had complete air supremacy, and knew the exact time, date and place of the meeting of the German officers, this mission would never have taken place. The brightly lit chateau would have been flattened by a squadron of heavy bombers. Lee Marvin, an experienced combat veteran, pointed this out to the producers and was told to keep his opinions to himself.