The cripple fight was an homage to They Live.
The animation is done with CGI; I believe they use the LucasArts system. That gives them a 5 day turnaround, as opposed to conventional animation (like The Simpsons) which requires 8 months per episode. That’s why South Park can be so current. They have always had the ability to show stuff as advanced as Star Wars: Episodes Crap, but have mostly stayed with the look and feel of cardboard. (They only used actual cardboard for the first episode about alien abductions.)
They don’t have to bleep out anything. They do it because it’s funnier. (Direct quote from Matt and Trey.) Similar to the movie title. The original title was a more blatant cock reference…something like South Park: Long and Hard. (Not it but equally unfunny.) After several titles were rejected by the MPAA or FCC or whomever, they finally came up with “Bigger, Longer, & Uncut”, which is a clearly funnier cock reference.
All this info I just recently learned from an hour long South Park interview/special on one of those channels…MTV, VH1, CC, E!; I can’t remember which one. It was in the vein of “Souh Park: Behind the Scenes.”