Mumbly bears a strong resemblance to his brother Muttley from the animated series Wacky Races and Dastardly and Muttley in their Flying Machines. Like Muttley, Mumbly does not really talk; he mumbles and grumbles unintelligibly, and often uses his trademark snicker. Detective Lieutenant Mumbly's boss is Schnooker (voiced by John Stephenson), an aptly named egotistical police chief who tries to take credit for nearly all of Mumbly's heroic deeds. Unlike Muttley, Mumbly has bluish-grey fur and wears an orange trenchcoat.
Mumbly may have been inspired by Peter Falk's TV character Columbo, as the two share a sartorial style and speech patterns. A further link is that Muttley was based on a similar premise to Peter Falk's character Max Meen in The Great Race, as noted in the Wacky Races article.
Ironically, Mumbly later appeared on the opposite side of the fence as the captain of the villainous Really Rottens on Scooby's All-Star Laff-a-Lympics / Scooby's All-Stars (1977–79), alongside Dread Baron, who bore a great resemblance to Dick Dastardly. Mumbly was the only member of the Really Rottens that wasn't created for Laff-a-Lympics. The good-guy teams, the Scooby Doobies and the Yogi Yahooeys, were composed of characters from previous cartoons. Mumbly would return as a villain alongside the Dread Baron (resembling the team of Muttley and Dick Dastardly) in 1987's TV movie Yogi Bear and the Magical Flight of the Spruce Goose.
In his villanous appearances, Mumbly's former occupation as a police detective is never referenced and there is no in-universe explanation for his retcon as a villain. Nor is Mumbly simply Muttley by a different name, although one episode of Laff-a-Lympics accidentally refers to Mumbly as Muttley in a script blooper. Whereas Muttley was consistently depicted as Dick Dastardly's sidekick and comic foil, Mumbly was depicted as independently clever and cunning in both his heroic and villanous appearances. Additionally, on Laff-a-Lympics, Mumbly was the leader of the Rottens team, with Dread Baron as his right-hand man.
The reason for the use of Dread Baron and Mumbly as substitutes for Dastardly and Muttley is not certain. The most commonly suggested reason is that the Wacky Races characters (including Dastardly and Muttley) were created as a co-production with Merrill Heatter and Bob Quigley Productions, meaning that they were not fully owned by Hanna-Barbera, and thus could only be used with permission.