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.
Alan Arkin not only played Inspector Clouseau, he played the members of the gang whenever they were disguised as Inspector Clouseau, with the other actors' voices dubbed onto the soundtrack.
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, at the time (or so he admits) believing 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.
The musical group Portishead sampled the soundtrack for their song "Only You" from their eponymous 1997 album. The specific music sting comes from the scene halfway through the picture when Closeau encounters two of the gang members in an alley.
The animated opening credits uses the character design of the Inspector from The Inspector (1965). This is notable as all the other opening credits of Inspector Clouseau's films had a design more faithful to Clouseau's actor (either Peter Sellers or Steve Martin).
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).
The three portraits on Braithwaite's desk (that he and Clouseau keep moving around) are of Queen Elizabeth II, Prince Philip and King George VI.