It's interesting to note that this is the first (but not the last) of the Pink Panther films to use the "Pink Panther" in the title, but without any connection whatsoever to the jewel by that name; in the humor as well as the title, it looks like this film is desperately reaching for the comic success of some of the earlier installments.
Two things make themselves apparent immediately. One, the humor in The Pink Panther Strikes Again has moved fully into the slapstick realm; we don't get any of the visual set-pieces, the occasional flash of verbal wit that livened up the earlier films, or the cleverly built-up absurd situations; the comedy is broader and cruder, and generally takes the form of one-shot slapstick moments. Two, a lot of the jokes are recycled from earlier Pink Panther movies. For instance, the "various attempts on Clouseau's life" is a rehash of the same sequence from A Shot in the Dark, but here it's more drawn out but also not nearly as well done. (On top of that, we get a lot of recycled jokes even within the film: just count how many times "character falls in the water" is used as a big gag.)
There are still some funny moments in The Pink Panther Strikes Again (Clouseau and the parallel bars; the first scene with Cato; Clouseau resuscitating Dreyfus; the Steinway piano incident). By and large, though, they are just that – moments – rather than funny scenes or situations. In fact, the credit sequence featuring an animated Clouseau and Pink Panther, is by far the cleverest full scene in the film. The plot itself is rather labored, and has a number of spots that don't stand up to scrutiny; for instance, the character of the Russian agent Olga feels shoe-horned in just to have the "gorgeous actress of the moment" in the film, and her ending scene with Clouseau feels blatantly like a desperate attempt to find fifteen minutes' more footage to tack onto the film. All in all, The Pink Panther Strikes again isn't exactly bad, but it's undeniably bland.