Continuity mistake: When the protagonists are trying to get to the French embassy they pass a VW beetle whose windshield is smashed by a Red Khmer. The camera angle is not very helpful but if you look closely you see that the window is gone already, and the pieces flying over the hood are from the bit of glass that sticks in the frame. (00:56:50)
Factual error: During their transatlantic boat trip, on their way to Athens, the American athletes are having fun naming various foods from back home that they already miss. One of them claims he misses chocolate chip cookies. Oops. That particular cookie didn't exist until Ruth Wakefield invented it in 1930.