Stunt Casting: In perhaps the biggest example of this in Simpsons history, Elizabeth Taylor as the voice of Maggie. (Taylor returns at the end of Season 4 as herself in "Krusty Gets Kancelled", and gets two lines in that episode.) The writers soon regretted this as they spent hours trying to get Taylor to say, "Daddy" like a one-year-old child and not a 20-to-30 year old seductress.
The Other Darrin: When the ending of the episode was put into the clip show episode "Gump Roast", Liz Taylor's "Daddy" line was replaced with the same line as done by series regular Nancy Cartwright (who usually does vocal effects for Maggie, such as crying, cooing, and laughing).
Throw It In!: Homer's line, "Bart can kiss my hairy, yellow butt" after Marge express worry about Bart being jealous of Lisa was ad-libbed (and almost didn't get used as the censors thought the line would be construed as pedophilic, when really to tell someone to "kiss your butt [or ass]" is used as a rude brush-off, not a sexual come-on. Of corse, it's now one of the most popular phrases to put on Simpsons merchandise).
Write What You Know: The scene where Homer builds a scary clown-shaped bed for Bart was inspired by writer Mike Reiss, whose dad had built him a clown-shaped bed when he was younger, and just like Bart, Reiss was scared of sleeping in it.