Bugs Bunny's hunched-over walk and eyebrow-wagging are imitations of Groucho Marx. The evil scientist is a caricature of long-time character actor Peter Lorre. The other contemporary actors to be represented are: Boris Karloff (silhouette which responds when they ask for a doctor... Dr. Frankenstein) and Edward G. Robinson (the caricature in the framed picture, whose eyes follow Bugs Bunny).
This was the final appearance of Chuck Jones' Bugs Bunny design, as starting with his next Bugs Bunny cartoon, A Feather in His Hare (1948), he would use Robert McKimson's design for the character.
The orange monster has no name in this cartoon. He is known as Rudolph in Water, Water Every Hare (1952), then as Gossamer in Duck Dodgers and the Return of the 24½th Century (1980). The latter name is the one most familiar to cartoon fans.
Bugs says that monsters lead such interesting lives. This line would become a song in the cartoon short The Night of the Living Duck (1988), sung by Daffy (with some help from Mel Tormé).