The actual answer to the algebraic equation the Chicken/Squirrel is trying to solve is: X = 8 - Y
The half chicken/half squirrel does not understand algebra, as its working was totally off (2x-y=y-3 does not equal 2x=-3).
In this episode we learn that Kyle believes in Peter Pan.
The head of the "half chicken/half squirrel" is actually the head of a rooster.
Cartman: You guys, you guys! Oh my god, seriously, you guys!
Stan: What the hell's wrong with Cartman?
Kyle: He's fat and stupid.
Kyle: But you know, I've learned something today. You see, the basis of all reasoning is the mind's awareness of itself. What we think, the external objects we perceive, are all like actors that come on and off stage. But our consciousness, the stage itself, is always present to us.
Mr. Foley: I'm going to find out who the boss is, and when I do, I'm going to bust his ass and everyone's ass who helped hide his ass!
Loogie: They're what!? They're not going to pay me? Who the hell do they think they are? I want those South Park kids dead! I want their families dead! I want their houses burnt to the ground!
Chef: Well whatever you're doing, just remember this: Having money may seem fun but……Oh never mind.
(When Cartman throws the wad of money to Chef)
Chef: Oh my God! There's got to be at least 15 dollars here!
Dentist: Anyway, the half-chicken, half-squirrel would most likely be about 3 to 4.5 feet tall. His large beak is probably detachable and works as a flotation device.
Mr. Foley: It's not ridiculous, it's very possible! I've seen it happen before!
Mr. Foley: In Montreal.
(All of the dentists burst into laughter)
Dentist: And where, pray, is this Montreal?
Dentist at ADA: …We believe that there can be only one logical reason for all of this.
(Slide changes to show the reason)
Dentist at ADA: A giant half-chicken, half-squirrel that steals either teeth or money from children as they sleep in order to build some kind of giant nest for its genetically superior and potentially dangerous offspring. We believe also that this creature would have at least a mild understanding of algebra and that it…
(interrupted by other dentist)
Loogie: Tell you what, how would you like to run the South Park tooth racket for me?
Stan: Oh. I dunno…
(Loogie holds up a knife)
Loogie: It's that, or else I can cut off your penises.
Cartman: Hmm. Work for you…Have my penis cut off. Work for you…Have my penis cut off. Let's see…
Cartman: Man, that is tits!
Loogie: Kids have been doing the tooth fairy rack in this town for years. I do it just like my big brother before me, and my oldest brother before that.
Cartman: It's better than your dress. You look like a bad Jennifer Lopez nightmare!
Cartman: Yea! This is so tits!
Cartman: How do you know what the tooth fairy wants me to do? You're not the tooth fairy!
Cartman: My mom lied to me just like your parents lied to you and now we're poor like Kenny's family.
(Kenny walks over to comfort Cartman.)
Cartman: Don't touch me Kenny.
(Sick kid talking to parents while Cartman lurks outside his window.)
Sick Kid: Oh mommy, I can't wait to be better!
Cartman: Well kid, you're gonna have to wait just a little longer because that $600 is mine.
Chef: Well look at you cute little crackers with your money and your fancy clothes and your cell phones. It's almost like you were…Oh my God! Children, what have I told you about drugs?
Stan, Kyle, Cartman, and Kenny: There's a time and a place for everything and it's called college.
Kyle: What about Dan Rather? Do you think he's real?
Cartman: No, man, that's just a TV show.
Cartman: (telling Butters as the tooth fairy) Do not open your eyes until morning, or I will kick you in the nuuuuuts…square in the nuuuts.
Cartman: I love that song, mom. Sing it again.
Liane Cartman: No honey, mommy's got to save her throat. I have to work tonight.
News Anchor: …to which Mrs. Clinton replied, 'I don't even like vagina.'
The music playing behind Kyle when things start to trip out towards the end after he realizes his reality is "Pork Soda" by Primus and "Welcome To This World" by Primus, the band who does the show's theme. Both songs are off their 1994 album Pork Soda.
This is the first time since the South Park movie that we see Kenny not in his parka (we can not see his face, however...).
According to Matt and Trey on the commentary for this episode on the DVD, Timmy was a huge fight with Comedy Central standards, but he eventually was let in. Two weeks later, "Timmy 2000" aired with another fight, except after this one, Timmy became hugely popular, leading Comedy Central to tell standards to issue no Timmy complaints so they can sell more merchandise.
When Loogie is explaining how the tooth trade works, scenes of various kids are shown putting teeth under pillows, taping notes to doors, and collecting money. One of the kids collecting money is Timmy, wheelchair and all.
This is Timmy's first appearance.
The books that Kyle reads in this episode are: "Space-Time and Quantum Theory", "Taoism and Zen Philosophy" and "Descartes". (Rene Descartes was a French philosopher and mathematician.):
Welcome To This World:
The songs used during Kyle's discorporation is a mix of "Welcome To This World" and the title track from Primus' fourth album Pork Soda.
Chikyuu Sentai Fiveman:
There are stickers on the rich kid's window that are referred to as Mega Man stickers, although when the boys try to break into his bedroom to plant a tooth they appear to have helmet designs of the Chikyuu Sentai Fiveman.
Loogie is clearly based on Marlon Brando's character, Vito Corleone in The Godfather movies.
Pink Floyd The Wall:
When Kyle alternates reality and changes between shapes such as a donkey and cheese, is a reference to the 1982 Pink Floyd movie, The Wall, because it containes a scene in which a main character Pink changes form in a very similar way.
Loogie: I want those South Park kids dead, I want their families dead, I want their houses burnt to the ground!
This quote is a play on the quote spoken by Robert DeNiro as Al Capone in the 1987 film The Untouchables.
Kyle: This book says I don't exist unless I think I do.
Kyle is reading Descartes Meditations on First Philosophy. Descartes casts all his beliefs into doubt, but in the second meditation he finds one belief he cannot doubt: I think, therefore I am. But it is only necessarily true while the thinker is thinking.
2001: A Space Odyssey:
When Kyle does his little "transformation" after realizing nothing exists, his final "form" of it is an odd fetus, like David Bowman did in the 1968 film 2001: A Space Odyssey.