Character mistake: In the film, five items are stolen: the Magna Carta, the Turin Shroud, the Imperial Sword of Japan, the Pope's ring and the Pink Panther diamond. When Alfred Molina's character is challenged that they had found everything but the Pink Panther, he protests that 3 out of 4 is not bad, that's 75%. In fact, they had found 4 out of 5 or 80%.
Continuity mistake: Towards the end of the movie when Sonia was trying to escape, after Clouseau figures out that she stole the pink diamond. Sonia Is trying to escape and runs up through the kitchen to the second floor and is passing through the balcony. In one quick shot her red dress is exposing her right shoulder when in the rest of the scene it exposes her left shoulder.
Other mistake: Inspector Clouseau concludes Miss Solandres was the thief by looking at her license plate and discovering he gave the car a fine 2 days before she claimed to have arrived in Paris, 1 day before the Pink Panther was stolen. However she told Clouseau her car was a rental moments earlier, therefore he should've assumed the fine applied to the previous renter as Clouseau had no reason to doubt Miss Solandres' story at that point.
Continuity mistake: During the restaurant scene in Rome, the Inspector insists on selecting the wine. He picks the first bottle from the middle of the wine rack. In the next shot, the slot is full and he places the bottle in a higher slot. In the third shot, he picks up another bottle from the middle of the rack.
Continuity mistake: When Clouseau is going to meet the "Dream Team" for the first time, he walks across the hall with Ponton and Nicole. We can see the cage from where the Pink Panther diamond was stolen as they approach it and it is clear that it is empty, but in the next shot the door opens and we see the detectives already inside the cage.
Revealing mistake: In the scene at the Pope's apartment, when Clouseau enters the balcony for the second time to "look at the moon", there is a third shot from his back when he is leaning out of the balcony. You can see a platform which supposedly was there to help him easily fall out.