The Big Giant Head (William Shatner) says, "I'm a rocket man you know?" In 1978, Shatner performed a spoken word rendition of Elton John's "Rocket Man" in his classic over-paused, over-acting style.
The Big Giant Head (William Shatner) says that he looked out the window and saw something on the side of the airplane he flew in on, whereupon Dick (John Lithgow) exclaims, "The same thing happened to me!". This is an inside joke about The Twilight Zone story "Nightmare at 20,000 Feet", which is about a frightened airline passenger who sees a gremlin on the wing of the airplane he's flying on. Shatner played the lead role in that 1963 episode of the TV series The Twilight Zone (1959), and Lithgow played the lead role in that story in Twilight Zone: The Movie (1983). Additionally, Dick (Lithgow) also saw something on the wing in season 1: Frozen Dick (1996).
At one moment John Lithgow is dancing in a bar to the song Footloose. John Lithgow played the part of Reverend Shaw Moore in the film Footloose (1984).
Joseph Gordon-Levitt (Tommy) and Larisa Oleynik (Alissa) portray high school love interests who attend the prom together. They also portrayed high school love interests who attend the prom together in 10 Things I Hate About You (1999).