When Homer accidentally drives into a deer statue, Homer responds with "D'oh!", quickly followed by "A deer!" by Lisa and "A female deer!" by Marge. This is a reference to a song in the film
When Lisa gets told she can be a tutor, she dances on a hilltop similar to the opening sequence of the film) and when she introduces herself, Cletus' children walk forward and state their name (a reference to Maria's introduction to the children). Some of the songs they sing are based on songs from the film, including the song performed by Superintendent Chalmers and Principal Skinner, which is inspired by "How Do You Solve a Problem Like Maria?" Lisa sings part of a song resembling "The Sound of Music", and later while showing the children the culture of Springfield sings a song based on "My Favorite Things."
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