Alan Arkin got the role of Clouseau because Peter Sellers was busy doing The Party (1968), directed by Blake Edwards, who was also the director of the previous Clouseau films. He was replaced by Bud Yorkin. Later, Sellers and Edwards would return to the series. With them, the original composer (Henry Mancini) also returned.
This is the only film in the original Pink Panther series not to be directed by Blake Edwards or be composed by Henry Mancini.
With Peter Sellers adamantly refusing to return as Inspector Clouseau, Alan Arkin was approached, following his big success with The Russians Are Coming the Russians Are Coming (1966). Arkin accepted, believing at the time (or so he admits) that he could do any role offered to him. The film's dismal box-office performance taught him to be more humble and cautious, and he has considered this film to be a mistake.
Alan Arkin not only played Inspector Clouseau, but also played the members of the gang whenever they were disguised as Inspector Clouseau, with the other actors' voices dubbed onto the soundtrack.
In the scene where Clouseau is being chased through the cemetery after falling in the plot and disrupting the funeral, you can see a sign on a cross in the lower right part of the screen for a few seconds. The sign reads "Reposite En Pace: Norman Lear, 1903-1962". This is an in-joke that refers to Norman Lear, who was director Bud Yorkin's producing partner for many years on shows such as All in the Family (1971) and Sanford and Son (1972).