This episode's title is a reference to Jack and the Beanstalk. Several elements of the episode refer to the fairy tale.
Leela's imprisonment in the tower and letting down of her 'hair' to allow Fry and Bender to climb up refers to Rapunzel.
As Fry and Bender are climbing up to Leela, they encounter Adam West and Burt Ward at a window; this parodies a moment in various episodes of the Batman TV series, when the Dynamic Duo would similarly encounter a celebrity as they climbed the side of a building.
Jake the Dog and Finn the Human from Adventure Time are seen chained up in Momsanto.
The scene in which the Hyperchicken is saying that the sky is falling could be a parody of Chicken Little
A plaque with Momsanto seen in this episode is a reference to Monsanto, a genetic engineering agriculture company.
Leela refers to the Monsanto castle as "some kind of de-luxe apartment in the sky", a reference to the theme song for the sitcom The Jeffersons.
Mom refers to her mutant bean plants as "Colossus, The Beanstalk Project"; the name references Colossus: The Forbin Project, a 1970 film based upon the 1966 novel, Colossus.
The country bar is called TEX 1138, spoofing THX 1138, George Lucas' first movie.
We find out in this episode that Leela occasionally lays an egg.