The opening scene of Brain lying face down in the water is a reference to the classic film 'Sunset Boulevard.'
The "she's a mouse! She's a hamster!" scene is a takeoff on a famous scene from 'Chinatown.'
Snowball has a painting of himself as Gainsborough's Blue Boy.
Brain says "The world can wait," which is also the title of the 'Pinky and the Brain' cartoon in which Billie first appeared.
Sam Spade is a famous detective created by Dashiell Hammet.