Creator Backlash: In addition to a noted dislike of the South Park video games made early in the show's run (one of which, for the Nintendo64, managed to make a 2003 G4 list of "most spectacular failures"), Trey and Matt were not happy about the "201" censorship.
Creator Breakdown: Trey Parker had a hard time forgiving his ex for cheating on him and it shows in a lot of his work:
Cannibal! The Musical has Matt and Trey providing commentary, during which Trey gloats over how he's now a famous comedy writer and his slut of an ex is now dating a nobody.
The Cartman's Mom is a Dirty Slut two-parter: No prizes for guessing who Liane Cartman is based on.
The Love Dodecahedron in Team America may also have been influenced by this, as Lisa is the one who cops the most abuse for sleeping with Gary.
Raisins (the season seven South Park episode where Stan turns Goth after Wendy breaks up with him and Butters thinks a waitress at a Hooters-style restaurant for kids actually likes him) may have been an indicator that Trey has since learned to let go and laugh about it... then The Ring (the season 13 premiere in which Kenny dates a fifth grader with a seedy reputation who gets Kenny to join a purity ring program after seeing The Jonas Brothers in concert) happened.
Magnum Opus Dissonance: Despite their hate for the show's first three seasons (with season 2 as their most hated. It's so hated that they didn't even do audio commentary for it on the DVD set), Parker and Stone also state the second season episode "Not Without My Anus" (the episode that centered on Terrence and Phillip getting their child back from Saddam Hussein) to be the only episode they liked from said era, because it was "something weird and different." Even stranger considering the episode generated a lot of fan backlash, and that the first three seasons are home to many of the show's most memorable episodes according to critics and fans.
Trey and Matt feel this way about the show's first three seasons, as noted in an interview for Entertainment Weekly, "it's just embarrassing to watch." In one of the commentaries on the season 3 DVDs, the duo mentioned that they considered season 2 to be particularly bad.
Trey is an admitted Japanophile (and majored in Japanese studies in college). The South Park episode "Trapper Keeper" directly parodies Tetsuo's meltdown in AKIRA, the Japanese spoken in "Chinpokomon" is accurate, and "Good Times With Weapons" is an Affectionate Parody of shonenanime like Fist of the North Star. He went a step further and married a Japanese woman (though they have since divorced).
The show is also full of references to Star Wars and Star Trek, and both Parker and Stone are avid video gamers (hence the show's unusually detailed and accurate references to video games and game consoles).
Apparently, Parker and Stone were at one point asked to write the sequel to Dumb and Dumber.
They were also set to write a film called "My All-American" at one point, as well as one titled "Giant Monsters Attack Japan!". Both projects fell through, as they remembered how burnt out they got on Team America, as well as wanting to focus more on South Park and (eventually) The Book of Mormon.
Interestingly, "Giant Monsters Attack Japan!" would've been the first production of theirs that would've been appropriate for children, as they were aiming for a PG-rating.