Factual error: When Andy is in the club with his future manager in the audience, he tells the crowd (in his Foreign Man persona) that he is going to imitate President Carter. After hooking up with his manager, he gets a gig on the first episode of Saturday Night Live, which debuted in 1975. Jimmy Carter wasn't President until 1976.
Factual error: In the film, Andy plans the Carnegie Hall gig after learning he has cancer. The actual concert took place in 1979, when Kaufman's popularity was at its highest, not near the end of his life and career (1983-84). (Regardless of the writers' intent when writing the script for this film, it is still a factual error.)
Factual error: Andy didn't meet his girlfriend Lynn when he was wrestling women on the Merv Griffin show. They actually met in 1981-82, when his "wrestling career" was dying down (incidentally, if you rent the movie "My Breakfast With Blassie", you actually see Andy meeting, and hitting on, Lynn for the first time. They had never met prior to the filming of their improvised scene. It's pretty funny-rent it!)