The entire episode is a parody of the 1971 movie Willy Wonka and the Chocolate Factory, which is based on the book Charlie and the Chocolate Factory by Roald Dahl. The dance moves performed by the Grunka-Lunkas whilst they sing are all taken directly from the Oompa-Loompas in the movie and Glurmo is based on Gene Wilder's portrayal of Willy Wonka.
Glurmo's sudden appearance at the front of the rolling red carpet is a reference to Bugs Bunny's similar appearance as the King in "Rabbit Hood".
The "Soylent Cola" joke is a reference to the 1973 science-fiction film Soylent Green, starring Charleton Heston. The big surprise at the end of this film is that the most widely-distributed food, Soylent Green, is actually made out of people.
The Scrabble game between Leela and the Professor bears similarities to "tri-dimensional chess", as seen in Star Trek.
When Leela and the Professor are playing Scrabble, the Professor can spell the word "f u t u r a m" with his extra letters.
The cartoon gag in the episode is from The Tracey Ullman Show: Simpsons shorts episode, Making Faces.
When the queen suggests that Leela becomes the mascot of New Slurm and having it fail and bring back the original Slurm, is a reference to Coke changing to New Coke.
According to audio commentary, Glurmo's name was originally going to be "Slurmy Slonka".
Leela says, "Something's rotten on the Planet Wormulon." which is a reference to the famous quote by Marcellus in William Shakespeare's Hamlet.
While at the gift shop, Zoidberg is wearing a shirt written in Hebrew that reads "שלורם", which is pronounced "Shlurm".
The Wormulon Queen mentions that she plans to change the flavor of Slurm, and if the public dislikes it, she will bring back the original flavor for more money. This is based on how Coca-Cola did the same thing, by making a drink called New Coke, but brought back the original as Classic Coke as so many people disliked the new flavour.
Fry has apparently had heart problems in the past, as he apparently had at least three heart attacks when he was in high school (when he was presumably 14 to 18).
The Slurm contest rules written in Alienese say, "The following species are ineligible, space wasps, space beavers, any other animal with the word "space" in front of it, space chickens, and the elusive yak-face." The elusive yak-face is most likely a reference to a hard-to-find Star Wars collectible produced by Kenner accidentally. Since the character was originally just a background alien in Return of the Jedi for about three seconds, production was halted as soon as the oversight was discovered and the few that were made were sold in Canada and Europe.
The eye chart says: N O S Q U I N T I N G F O U R E Y E S