Shot in the Dark is the first in the series with Inspector Clouseau as the main character. The character was so popular in the first film, The Pink Panther, that the Phantom, Charles Lytton was downgraded to a supporting character and David Niven, who played the Phantom, left the series entirely. Shot in the Dark then plays to Peter Sellers' strengths as the greatest English comedic actor since Charlie Chaplin, the physical acting, the subtle body movements, the physical and spoken mannerisms of Clouseau as interpreted by Sellers. Clouseau is, of course, physically clumsy in the extreme and the pratfalls and slapstick associated with the character are liberally present. Clouseau is also occasionally maladept at the English language, e.g. "rheum," "bimp", maddening to his character interlocutors, hilarious to the audience. "A fit of jealous rage" is rendered "A rit of fealous jage" by Clouseau.
"YES!" Clouseau's clipped phone answering when he intends to be officious and authoritative.
This film also marks the debut of Cato, Bert Kwouk, and the iconic fight scenes. There are four in Shot in the Dark, complete surprises to the audience, and were so popular that Blake Edwards decided to be parsimonious with them in later films. Shot in the Dark is, from my recollection of the other Pink Panther films, more subtle in its physical comedy. There is a scene in the beginning where Clouseau twice hands his houndstooth hat to a Ballon household servant only to end up back with the hat a moment later. I had to rewatch the scene to catch how it happened.
"Three"
"Four".
Plain as the hand in front of your face, again I had to rewatch to catch the dissonance between the spoken word and the physical gesture.
A Shot in the Dark is the template and the franchise. It is overlooked because it doesn't have Pink Panther in its title.