Continuity mistake: During the interview with Maria, the Inspector's pants are torn when removing her file with a key on a chain, the Inspector's shirttail is exposed. When he walks back to his desk and calls his assistant on the intercom, the shirttail is no longer visible. When Hurcule returns after escorting Maria back to prison, the Inspector turns away from the window, and his shirttail is again exposed. (00:33:45 - 00:35:25)
Continuity mistake: During the interview with Maria, her headscarf disappears from Inspector Clouseau's desk. (00:34:28)
Continuity mistake: The balloons that Inspector Clouseau is carrying changes. For example, he has 3 yellow balloons when outside the prison but there are 4 yellow ones when the police van is driving down the street. (00:35:45)
Continuity mistake: At the beginning of the billiards game, Monsieur Ballon leans the "bridge cue" against the lamp. At the end of the game, when Clouseau is putting the cues away, it is leaning against the wall. (00:48:21)
Continuity mistake: When Clouseau is explaining how Maria got a bump on the head the yellow cushion on the sofa changes position. (01:33:57)
Continuity mistake: When Cato jumps Clouseau the first time, Clouseau's hands are on Cato's shoulders in a shot behind Cato. When the camera's on Cato, Clouseau's hands are suddenly on his throat.
Continuity mistake: Clouseau gets his left foot stepped on by Dominique Ballon causing him to hop around holding his left leg. A shot later he's holding his right foot.
Continuity mistake: Maria rips Clouseau's suit, and he tells her not to worry and starts pulling it back up. The shot cuts and it's back down again.
Answer: In this particular film, he's referred to solely as "Commissioner" and is then Chief Inspector in every subsequent Pink Panther film in which he appears (up until "Son of the Pink Panther" [1993], Herbert Lom's last appearance in the role, when he is again Commissioner). If you're after a reason, there likely isn't an official one, though perhaps Dreyfus's murder spree and mental breakdown in this film led to his demotion.