Factual error: At the end of the movie, Mame takes Peter with her on a trip to Siberia. However, at this point in the timeline, it's the late 1940s, meaning that Stalin was still in power, so even Auntie Mame would be crazy to think of vacationing in Russia. Not to mention the difficulties of getting Peter a visa to travel to the USSR at the last minute. (In the stage version, the destination was India, rather than Siberia, which makes a lot more sense).
Visible crew/equipment: In the apartment scene with Dustin Hoffman and Valerie Perrine, he prances in front of a vanity mirror, and a big boom microphone is right over his head, hanging deep into the shot, reflected in the mirror. The boom microphone is quickly retracted, so they knew they had made a mistake, but the shot remained in the finished film.
Factual error: As the airship approaches Astragard it's headed due North; yet the distant clouds are backlit by the Sun. The Sun should be to the South.
Revealing mistake: During the chase that opens the movie, the guy trying to escape shuts the door labeled "Back Stage" behind him. The various goons try to push it open, but only the badass villain with the charismatic afro can do it using his palm strikes. Sort of though, because just before he shows up in front of the door, you can see the door was unlocked and opened under the push of the normal minions, with the light fully showing between door and frame. (00:03:10)
Continuity mistake: In the opening scene, Irwin Ingham's big scarf is wrapped around his neck in ever-changing fashion as it can be spotted looking at the striped area being at different height each time. (00:03:40)
Continuity mistake: When Buster and Billie are at Slim Mim's Jamboree near the end of the film, Buster is wearing an open-collar shirt. When they step outside to get some air, it changes to a button-down shirt and tie.
Continuity mistake: When the boy stabs the man in the back with an ax while they're chopping firewood, the position of the ax changes between shots. In the first shot, the ax is vertical because the boy is behind the man. In the next shot, the ax is horizontal as if the boy is on the right side. (01:06:53)
Continuity mistake: Nini's mother fishes the telephone out of the bathtub. A naked little boy prances around the room and Christian De Sica is in a quite recognizable position, leg up scrubbing the sole of his foot. Cut, and De Sica is now simply sitting in the tub as if nothing happened. (00:22:00)