Creator Backlash: The unanticipated workload of an all-marionette feature, attempting to make a studio blockbuster as spontaneously as a South Park episode and the compromises they had to make in order to have total creative control convinced Trey and Matt that they never wanted to make movies ever again.
Doing It for the Art: Sort of. Trey and Matt forfeited their salaries in exchange for complete creative control from Paramount, feeling that they didn't really need the money. The drawback was that they had nothing to look forward to on days when they were particularly burned out.
Talking to Himself: This happened a lot. There were only 10 voice actors in the entire movie, and Trey Parker alone did the voices of Gary, Joe, Kim Jong Il, Hans Blix, Carson, Tim Robbins, and the drunk in the bar.
Throw It In!: According to Stone and Parker, they hadn't originally planned to make Matt Damon any smarter or dumber than the rest of the actors guild. However, when his borderline-caveman looking puppet came in, they decided on the spot to make him a drooling idiot who could only say his own name, which Matt Damon himself thought was hilarious.
Troubled Production: Trey and Matt legitimately had no idea how difficult an all-marionette action film would be (judging by the source material) and clashed with the puppet-makers when they were told that even the puppetry that was meant to look bad on purpose took a considerable amount of puppeteering expertise and rehearsal that would not allow for the same kind of spontaneous script-changes that would come with making an episode of South Park. As mentioned above, they also forfeited their salaries in favor of complete creative control when Paramount started coming down on them about censorship, making them more apathetic to their already disillusioned vision. The result was Parker and Stone swearing off feature films for the rest of their lives.
Unintentional Period Piece: Much of the humor is directed against targets like Michael Moore, Kim Jong-il, the films of Michael Bay, anti-war celebrity activists like George Clooney and Sean Penn, and America's gung-ho behavior in The War on Terror, all of which were political and cultural touchstones of the year (2004) when the film came out. Now that America's (mostly) left Iraq and terrorism has faded from the agenda (until ISIS came along), it can feel rather dated, especially with Kim Jong-il's death in December 2011.
There seem to be a lot of conflicting stories going around as to what exactly the film's concept began as- some sources say Trey and Matt originally wanted to make an R-rated Thunderbirds movie, or wanted to remake either Armageddon or The Day After Tomorrow with puppets, while leaving the script entirely unchanged. Another story says it was originally written as a sequel to the cult film Megaforce.
Alec Baldwin and Matt Damon thought the movie was hilarious, and said they would've gladly lent their own voices if Matt & Trey had asked. George Clooney, who has done cameo voice work for South Park twice, was actually offended that they didn't make fun of him more. Even U.N. Weapons Inspector Hans Blix (who Kim drops into a Shark Pool) was amused.
Matt Damon was actually supposed to be portrayed as intelligent and articulate, but when Trey and Matt saw that his puppet looked "retarded" they decided to portray him as such.
The deleted scenes and animated storyboards show that the film was supposed to have slightly deeper character development, less subtle racism, and I.N.T.E.L.L.I.G.E.N.C.E. called F.O.N.Z.Y.