Continuity mistake: The President of the US is watching football on channel 1. Dreyfus interrupts the broadcast and an aide flips through the channels to discover that Dreyfus is on all of them - the TV ends up on channel 9. Throughout the rest of the scene, the TV switches back and forth between channels 1 and 9 without human intervention. (00:50:00)
Revealing mistake: When Clouseau is on the parallel bars, note the switch as he jumps and turns from Peter Sellers to stuntman, then note again as the stuntman falls down the stairs; the stuntman finishes falling behind the right hand side of the settee, and up pops Peter Sellers on the left hand side of the settee giving the apparant impression he has just fallen down the stairs himself.
Continuity mistake: At the very end of the film when the bed crashes through the wall, Olga has disappeared from the very first outside shot. She is then back to the left of Cato in the next shot. This was likely done because she was completely nude and the audience would've got a good look at her.