Continuity mistake: When the Pink Panther holds the "Here We Go Again" sign when hiding in the bear-skin rug, the eyes of the bear are completely different to the ones seen a few shots earlier.
Continuity mistake: When the Pink Panther is sleeping on the bear-skin rug, the price tag reads "$350-00." When he rides in the rug, the two end zeros have disappeared, and in the shot after that, they are back again.
Continuity mistake: When the janitor sweeps the floor litter into the tiger-skin rug, the Pink Panther ejects the litter and you can see that the janitor's sweeping brush and litter are by the rug when he runs off to fetch a gun. But when the janitor returns with a gun, the litter and sweeping brush have disappeared.