The first portion of this episode, "Whatever Happened to Baby Brain? is a parody of the movie "What Ever Happened to Baby Jane?". Also to the late beloved legendary Shirley Temple. Also the song "Nice Boat, Candy Cane" is a parody of her famous song "Good Ship Lollypop".
The man who kicks Brain out of the drug store is W. C. Fields, who famously hated children (in his act, that is).
Several real-life Hollywood icons are parodied, including Shirley Temple, W. C. Fields, Irving Thalberg, Bill "Bojangles" Robinson, Hedda Hopper, Mickey Rooney, and Orson Welles (who is, of course, the inspiration behind Brain's voice and personality).
The woman who answers the phone during "Just Say Narf" (when Pinky sings "call Detroit") is Diana Ross, a staple of Detroit-based Motown Music.
The song "Just Say Narf" is a parody of "Make 'Em Laugh" from 'Singin' in the Rain' (a song which, itself, is little more than a copy of Cole Porter's song "Be a Clown").