Other mistake: In the final scene where the police chief is barreling through the hospital on his bed, he goes along a straight path, yet when the two inspectors and the assistant come down the stairs they come out the side of the corridor. If the police chief followed a straight path, how did they come out of the side of the corridor, and how did the bed turn around a 90 degree corner at that speed?
Suggested correction: At 1:27:46 Inspector Dreyfus' hospital bed blows through a set of blue hospital doors. At 1:27:51 we see from a different angle, those same doors still partially open but swinging shut and then at 1:27:55 we see Inspector Clouseau and the others emerge from a different hallway, the blue hospital doors now shut behind them. Inspector Dreyfus' bed never made a turn as evidence by the doors. The trio though, for some reason took a different route chasing his bed.
Continuity mistake: When Dreyfus is holding the ice-pack to his eye, the angle changes to show Clouseau entering. In this shot Dreyfus removes the ice-pack, but in the next shot he is still holding it to his eye.
Suggested correction: Look again. He picks it back up off his desk.
The mistake is valid. He lowers his hand, with the ice pack and in the next shot it's back up, meaning no time has elapsed for him to do so. And this happens before he ever sets the ice pack down.