"Bad Dream House" parodies a number of haunted house films. The opening image of the house shows that one side resembles the house from The Amityville Horror house. Much of the plot follows the events of the film Poltergeist, such as a scary tree right outside Lisa's bedroom, while the lighting of scenes using vivid colours is done in a similar manner to Suspiria, and the implosion of the house at the end a la House of Usher. The comparison to 2001: A Space Odyssey is also quite fair, although much more obvious references are made in later episodes.
Bart, as the Raven, knocks several of Edgar Allan Poe stories off the bookshelf, including "The Pit and the Pendulum," "The Tell-Tale Heart," and "The Purloined Letter."
The book "To Serve Forty Humans" is a reference to The Twilight Zone episode where strange aliens greet humans with a book, which translated means "To Serve Man," and solved all the problems of Earth. Curious Earthlings accept invitations of the aliens to see their home world and travel on their spaceships. One man accepts such an invitation, but is stopped by his coworker, who has properly translated the book and shouts, right as he's getting on a spaceship, "It's a cookbook!"
Even though he was long gone, Edgar Allan Poe is credited as a writer for this episode.
This is the first time the show has adapted a book into an actual episode (short in the Treehouse of Horror series).
The joke here being that Gandhi was Indian as in the Asian country, not as in American Indian. Incidentally, some of his ashes are buried in California, south of where Springfield was most likely intended to be by Matt Groening.
In "Hungry are the Damned," when the Rigellians are measuring the Simpsons's weight, along with Kang, Kodos, and Serak, there is a fourth unnamed Rigellian with them that does not appear for the rest of the episode.
In "Bad Dream House" the house chants, "Die, die, everybody dies." This line and its cadence were later utilized in the 2008 direct-to-video horror film Trailer Park of Terror.
In "The Raven", Homer was reading Forgotten Lore, Vol. II. This is a reference to the second line of the poem, in which the narrator is pondering "Over many a quaint and curious volume of forgotten lore."
Marge's warning at the beginning was put in, just because the producers genuinely thought this episode was scary for younger viewers and children.