In response to Marge staying in character as Blanche DuBois in order to rehearse, Bart also adopts a character, that of a Cockney (East Londoner). However, his use of "gulliver" to mean "head" is not authentic Cockney slang (the correct word is "loaf" [loaf of bread]), but Nadsat, the fictional slang which was invented by Anthony Burgess for his novel A Clockwork Orange.
This episode caused controversy with the state of Louisiana, who took offense to New Orleans being called "The Sodom and Gomorrah on the Mississippi," leading to the blackboard gag in the next episode, "I will not defame New Orleans." 13 years later, when Hurricane Katrina and its destruction made the news, this episode aired in the United Kingdom as a rerun. The episode, once again, garnered complaints. UK's Channel 4 made a public apology and, as a result, banned the episode from ever airing again (in much the same way Season 9's "The City of New York vs. Homer Simpson" was banned in America after the 9/11 attacks, though it did come back, albeit with edits).
When Maggie goes to get the pacifiers, the music and actions are references to the movie "The Great Escape."
The plot references the film A Streetcar Named Desire, especially when Homer stands outside and yells: "Hey Maaaaaaaaaaarge!" to Marge, whom he can see through the window of Flanders' house. This is a reference to the scene where Marlon Brando's character Stanley Kowalski yells "Hey Steeeeeeeeeeella!".
The scenes with Maggie trying to escape from the daycare center (and later, to get the babies' pacifiers back) reference the film The Great Escape, especially the music and the scene where Maggie plays with a ball in her "cell" to kill time.
When Homer, Lisa and Bart go to pick up Maggie from the daycare center, they see hundreds of babies sitting everywhere and sucking their pacifiers. Afraid but confident, Homer picks her up and leaves without saying a word. This is a reference to the film The Birds where the protagonists are confronted with hundreds of birds sitting on perches.
When Homer, Lisa, Bart and Maggie are outside, Alfred Hitchcock passes by with two dogs, in reference to a similar cameo the director made in The Birds.
In the crowd of babies if you look closely, one of the babies looks similar to Tommy from Rugrats.
Author and philosopher Ayn Rand is mocked throughout the entire episode.
During the play, right before Marge appears on the scene, Homer is playing with the playbill. This is a reference toCitizen Kane, when Kane's best friend Jedediah Leland is bored during Suzan Alexander's operatic debut.