Continuity mistake: Early into the movie Andy is taking part in a meditation session. There is a wide shot of the whole group, which is seated in four concentric circles. Andy is sitting in the second circle, with two more circles behind him. When the camera angle changes to a front shot on Andy the two people behind him have changed, and the outer circle has disappeared.
Continuity mistake: When the ABC President is told about the "problems with the technical requirements on the Kaufman special" Andy is yelling "It's my special. I have creative control." To the right of this shot, you can see the actor who plays the ABC president waiting, he is standing right by a blue marker and some steel beams. Three shots later, the ABC President enters the area. (This is in chapter 8 on the DVD.)
Continuity mistake: After he gets expelled from his spiritual retreat Andy is seen in his bed, with his body tightly tucked under the blanket and only the head sticking out. Then Lynne comes, stretches out next to him (on top of the blanket). Then it cuts to a close up of both of them and Andy puts his arm around her - impossible the way they were lying before.
Continuity mistake: When Lawler smacked Carrey off his chair in the David Letterman scene, the hit was so hard that it made Carrey's mouth bleed (you have to look very carefully). When he stands up and is shown close up again, the blood is gone. (Incidentally, the reason Lawler hit him so hard was that Carrey constantly stayed in character throughout filming, and taunted him relentlessly. Lawler decided he'd had enough.)
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Continuity mistake: When Shapiro comes to see Tony Clifton for the first time the MC goes to get him from backstage. Watch the guitar player on the right: first he is holding his instrument with his fingerboard pointing up, then in a wide shot horizontally, then again up as before.
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.
Continuity mistake: On his first entrance in 'Taxi' Tony Clifton does a few dance steps on a car. Even though he comes empty-handed (if you don't count the two ladies who are with him) all of a sudden he has a whiskey bottle in his hand, which disappears again in the next shot.
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!)