- The episode title is a pun on Mission: Impossible.
- "Do Shut Up" could be a parody of The Young Ones, a similarly chaotic Britcom that ran on English T.V. in the early 1980s. It was known for its lowbrow characters who shared a similarly dismal house, and spent much of the show bashing each other over the head with household items.
- The song playing throughout "Do Shut Up" is "No Feelings" by the Sex Pistols.
- The scene where Homer is licking bullfrogs on an island refers to the first verse of Pink Floyd's Comfortably Numb song from The Wall album. Marge calling "Hello, is there anybody in there?" over the radio even intones the melody.
- Also, a similar storyline was used in Family Guy, where several characters lick frogs and go into a strange hypnotic trance, similar to what happens to Homer in this episode.
- The telethon scene at the end features various FOX characters as phone operators, including Bender from Futurama and Hank Hill from King of the Hill.
- PBS characters who chase Homer through the streets include The Teletubbies (they fire lasers from their antennas), Oscar the Grouch (who is in his trash can), Elmo (who is sharing Oscar's trash can), Yo-Yo Ma, Mister Rogers, and Big Bird (who comes flying down, squawking angrily like a real bird).
- When Homer tries to hand out Bibles when arriving on the island, Qtoktok claims that they cannot read. However, when Homer unveils his casino, Ak is able to read the sign.