In the scene where Cartman is talking about giving Butters a Hitler, pay attention to the chair that Kyle is sitting on. For a second, one of the chair's posts is replaced with a tall skinny alien (that looks like the aliens from the first episode).
Specifically, this happens at 2 minutes and 40 seconds into the episode.
When Chris says "Oh alright!" to the persistent salesmen, Trey Parker accidentally uses Mr. Garrison's voice when he says that.
Cartman's mom isn't shown at all in the episode even though Cartman goes to Aspen.
Why did the teens cheer Tad when he approached to the stage of the center? The 'geeky but hot chick' said that everyone hates him, because his father wanted to destroy the center.
Where is Stan's sister during the episode? Why wouldn't she be included in the family vacation?
When the teenager in red said "Where are all kids supposed to go?" Look at Stan, you can see his mouth moved into some of the words.
When Butters tells Thumper "That's my face sir", Cartman has no ski goggles. But in the next scene, he does.
Kyle: Well, what do we do do now?
Butters: Let's dance!
(Butters starts dancing around)
Cartman: Butters, I hate you with every inch of my body.
(Ike crashes through building)
Thumper: Okay you see what he did? He french fried when he should have pizza'd. You french fry when you pizza you're gonna have a bad time.
Thumper: (to Butters) Hey little dude you got some crap right here. (points to face)
Butters: That's my face, sir.
Singer: The hours approaching, just give it your best
You got to reach your prime.
That's when you need to put yourself to the test,
And show us a passage of time,
Were going to need a montage (montage)
Oh it takes a montage (montage)
Show a lot of things happening at once,
Remind everyone what's going on (what's going on?)
And with every shot you show a little improvement
Just show it or it will take too long
that's called a montage (montage)
Oh we want a montage (montage)
And anybody who wants to go,
From just a beginner to a pro,
You want a montage (montage)
Even Rocky had a montage (montage)
Anybody who wants to go,
From just a beginner to a pro,
You need a montage (montage)
Oh it takes a montage (montage)
Always fade out in a montage,
If you fade out, it seem like more time
Has passed in a montage,
Tad: This is a song I wrote about Stan Marsh. (singing)
Stan. Darsh. Darshy Darsh.
Stan Darsh, Stan Darsh.
Stan Darsh Darsh.
Kyle: Stan, you can't let that Tad guy get to you. Screw him, dude.
Stan: Dude, he's got Heather!
Kyle: You don't even know Heather!
Cartman: Hey! Have you guys ever seen this trick? When someone's sleeping, you can take a glass of warm water, and you put their hand in it - (puts Butters' hand in water)
Stan: Yeah, and then what?
Cartman: And then, you pee on them. (pees on Butters)
Kyle: No, dude, you're supposed to put their hand in warm water and it makes them pee!
Cartman: Oh, really? Oh well. (continues peeing)
Stan: Look I can't explain it but I have to do this. I'm not gonna die. I mean, how bad can the K-13 be?
Mechanic: The K-13? You don't want to go down that run. That run has got a history. 35 people have died goin' down it, and some say you can still see their ghosts up there. It was on that very ski run that a group of students were killed by a wolfboy who escaped from a mental institution. You see, that ski run was once a burial ground to a tribe of vampire Wichicaw Indians who ate the flesh of children with no eyes. Yah, a lot of history on that ski run.
Stan: ...Thank you.
Thumper: All right, little dudes, great to see you out here. My name is Thumper, and I'm gonna be your cool ski instructor.
Cartman: (to Stan) His name is Thumper?
Thumper: Okay, let's have the little dude at the end try first! What's your name?
Thumper: Okay, Mike, ski down to me!
Time Share Person: The police, the mayor, the president of the United States. Perhaps now you see the severity of your situation. I think we shall all sit down and listen to the presentation.
Randy: Well, our boys do seem to be spending a lot of time together lately. I think ever since their friend, Kenny, died they've been looking for someone to fill the void.
Chris: Well, our son is a perfect void-filler!
(Tad & Stan are about to race)
Tad: Ha! You're going down, little boy!
Stan: Yeah, probably.
After the second ski race a version of the Simple Minds' song "Don't You (Forget About Me)" is played.
John Hansen, future voice of Mr. Slave, is the one who sings "Take On Me" by A-ha in the end credits.
The song "Montage" was later reused in Trey Parker and Matt Stone's movie, "Team America: World Police."
The wise old man from "Butters' Very Own Episode" appears in this episode.
Some of the teen ski movies that were alluded to in this episode include "Aspen Extreme", "Hot Dog: the Movie" and others. IMHO, the best movie of this bunch is "Better Off Dead…".
While the boys are on the Bunny hill, their ski instructor's name was Thumper, which was the name of the bunny from the Disney animated feature Bambi.
When Stan trains for the second ski race, a movie technique called "montage" is used. Usually backed by highly energetic music, featuring little or no dialogue, a montage shows the progression of a character from novice to pro, in short sequences. This has been used in many movies and TV series, especially in the 80s. Examples that are spoofed here are Karate Kid (I and II) and the Rocky movies.
Check out the lyrics to this montage's song in the "Quotes" section of this episode - it quite literally mocks the whole concept of a montage.
For Dummies Books:
When Stan is trying really hard to learn how to ski down K-13, him and the girl read a book called "Skiing for Dumba**es." That of course is a take-off of the book series called "_____ for Dummies."
Team America: World Police:
The "training montage" song was also used in the 2004 film, Team America: World Police, which was created by South Park's creators, Matt Stone and Trek Parker.
When the parents are trying to leave the room to avoid the time-share guys, they can't avoid them was just like the final episode of Twin Peaks, where the main characters couldn't avoid the midget. They would go to a new room only to encounter the person (or people) they were avoiding.
Jud Crandall/Pet Sematary:
The man telling Stan about K-13 is a parody of Jud Crandall, a character in Stephen King's 1989 film, Pet Sematary.
This character has been used in several episodes of South Park.
The heads on the "geeky but hot girl"'s chest are inspired from elements of the 1990 film, Total Recall.
Breakin' 2: Electric Boogaloo:
The whole side-plot about the kid's rec-center is a parody of the 1984 film, Breakin' 2: Electric Boogaloo.