Author Existence Failure: Peter Sellers died during planning of the unmade Romance of the Pink Panther. Initially there were plans to film it anyway as a Dudley Moore vehicle, but he wanted Blake Edwards to direct it, and he didn't like that script; Moore moved on while Edwards made Trail and Curse instead.
Cash Cow Franchise: Even more so when you add in the animated spinoffs and their associated merchandise.
Peter Sellers was an Englishman playing a Frenchman, but beyond this, the character of Clouseau affects several disguises in the course of the series that require him to be various other highly-caricatured nationalities.
Herbert Lom (Commissioner Dreyfus) and Graham Stark (several roles) are also Eastern-European and British respectively. Sellers and Lom already co-acted together in The Ladykillers.
Fake Russian: Lesley Anne-Down (British) as the Russian spy Olga in Strikes Again.
Franchise Killer: Oh, boy. Where to even begin? This franchise was killed at least three times in its history. The original series was killed by the one-two punch of Trail of the Pink Panther and Curse of the Pink Panther (both of which were made without Peter Sellers' involvement; he had died by that point), both of which were box office failures and lambasted by critics. A decade later, an attempt to resurrect the original series with Son of the Pink Panther ended up becoming an enormous failure and sealed the original series' fate for good. The Continuity Reboot series with Steve Martin had an even shorter life. While the first film did well at the box office despite negative critical reception, the sequel three years later not only received more negative critical reaction, but it ended up under-performing the first film and put the series back on the back-burner once again. Time will tell whether or not the series gets rebooted yet again.
Money, Dear Boy: Partial motivation for Sellers being willing to reprise the role of Clouseau in the 1970s. (The other was getting enough clout to get Being Theregreenlit.)
Old Shame: Alan Arkin, not surprisingly, considers making Inspector Clouseau a mistake. He has rarely spoken much about the film in the years since, but one time Arkin did explain why he took up the role. In the late 1960s he was becoming a fairly well-known actor and thought that as a movie actor, he could do whatever role was offered to him, and he could do it easily. He admits that the failure of Inspector Clouseauknocked him off his high horse.
The Other Darrin: The Clouseaus besides Sellers, of course, but several other recurring characters were played by different actors from film to film (see the trope entry) in the classic series. In the rebooted series, Kevin Kline played Dreyfus in the first entry, but was replaced with John Cleese in the second.
Prof. Auguste Balls is an odd example, since essentially two actors took turns playing the part: he was originally played by Harvey Korman in The Pink Panther Strikes Again, but his scenes were cut from the film. The character makes his official debut in Revenge, played by Graham Stark. However, the following movie, Trail of the Pink Panther uses the deleted scenes from Strikes Again, and thus Prof. Balls is now Harvey Korman, a role he reprised for Curse...only for the character's final appearance to have him played by Graham Stark again.
Graham Stark, a close friend and colleague of Sellers, appears in all the films from Shot through Son (save for Inspector Clouseau) as various characters, two of which, Hercule and Auguste Balls, are recurring.
Robert Loggia plays an American gangster in Revenge and the current head of the French mob in Trail and Curse.
Composers: For the theatrical shorts, Bill Lava composed for every short from 1964 to 1966. He was succeeded by Walter Greene, who only scored a few cartoons before his cues (plus some by Lava) were recycled for every short well into the mid 70s. By 1978, an uncredited Steve DePatie started composing new cues that were used until the series concluded in 1980.
The original shorts have had quite a few DVD releases, but of the spinoffs, only The Inspector has also been released; the others wait in limbo.
Pink Panther and Sons is presumably held by Warner Bros. Television (they hold the rights to the Hanna-Barbera library, Turner Broadcasting having bought H-B in 1991 and Turner having merged with Time Warner in 1996- ironically, Turner had acquired a majority of MGM's backlog of stuff in 1986), so barring an agreement between them and MGM, it's off the table for now.
For the 1993-95 series, it's available only via dodgy torrent sites in Eastern Europe. You could get a DVD at one point, but it was only of season 1. The complete first season is available on Amazon.de, if nowhere else. A chunk of the show is available on the official YouTubepage.
Recycled Script: A number of 1970's cartoons, namely "The Pink of Arabee", "Pinky Doodle", and "Rocky Pink", would respectively be re-issued as "The Pink of Bagdad", "Yankee Doodle Pink" and "Pet Pink Pebbles" with new music and additional footage.
Role Reprisal: John Byner came back to voice the Ant and Aardvark for the 1993 series.
Screwed by the Lawyers: For Pink Panther and Sons; the many spin-off shorts aside from The Inspector and possibly The Ant and the Aardvark) might also be in this trope, given that MGM hasn't distributed them in years and the fact that the DFE library is fractured (currently the non MGM and WB stuff is owned by Disney; DFE eventually turned into Marvel Productions (owned by Marvel Comics), which got absorbed into Saban Entertainment, which then got bought by Disney in 2001 alongside Freeform and Fox Kids).
The Merch: In an odd example, the Pink Panther character is the mascot for Owens Corning insulation and was the mascot for Sweet'n'Low artificial sweetener.