The name of Grumpy's boat, the Grump-Tiki, is based on Thor Heirdall's boat the Kon-Tiki, in which he made his famous ocean voyage.
When he's narrating his Captain's Log, Grumpy adopts the exaggerated speech patterns of William Shatner as Captain Kirk from 'Star Trek.'
Before setting sail, Grimm appears dressed as the title character from 'Gilligan's Island.' Hildy refers to him as "Little Buddy," which is what the Skipper called Gilligan on the classic series.
Grumpy retrieving the cheese from the cave recalls Indiana Jones attempt to remove the idol from the temple in the opening sequence from 'Raiders of the Lost Ark.' His line "Mice. Why did it have to be mice?" is a take off on Indy's famous quote about snakes.
When Grumpy is posing as a fortune teller, he wears a cape and turban similar to those worn by Johnny Carson when he played Carnac. Happy imitates Carson's sidekick, Ed McMahon, when he says "you are correct, sir!"