Delia Boccardo receives an "introducing" credit
Alan Arkin got the role of Clouseau because Peter Sellers was busy doing The Party, directed by Blake Edwards, who was also the director of the previous Clouseau-films. He was replaced by 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.
Clouseau's coat and hat were introduced in this movie and stayed part of the franchise.
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 and Sanford and Son.