These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Anvilicious: Dicks (hawks) are necessary because assholes (general threats to people) need to be fucked (dealt with) before they shit on (blow up) everything, but pussies (doves) can get full of shit too, becoming assholes. Pussies are necessary because without them, dicks "fuck too much (There Is No Kill Like Overkill) or fuck when it isn't appropriate (Disproportionate Retribution)." In short, extremism is bad, m'kay?
In political terms: "dicks" = conservatives; "pussies" = liberals; "assholes" = rogue states/extremists
Awesome Music: Harry Gregson-Williams deliberately scored the film completely straight, as if it was a real action movie, to help sell the satire. It works perfectly in the movie, but out of context, the score is genuinely exciting and rousing.
Matt and Trey made the sex scene as dirty as possible, dirtier than they wanted it to be knowing the MPAA would want them to cut stuff out of it.
The scene where a very drunk Gary vomits outside the bar. Starts out at "small amount", then moves up to "disgusting but realistic", then graduates up to "large amounts", then "absurdly large amounts", then finally settling for "high pressure projectile vomiting at the camera and a puddle of the stuff at least 5 meters across". Don't forget the dramatic music.
There's even word that Kim Jong Il himself saw this film and was tickled by it, saying something along the lines of "This is a very funny movie." On the other hand, there's also word he wasn't impressed and tried to convince the Czech Republic to ban the film (for what it's worth, this is what Wikipedia has to say on the matter).
Hans Blix referenced his portrayal in the film (which he appears to have found as humorous as it was intended) in a recent lecture.
Most of the actors that were parodied loved it, and just about all of those actors stated for the record that they wish Parker and Stone had contacted them so they could voice themselvesacting like pussies.
Alec Baldwin cracked up when his daughter's classmates quoted Kim Jong Il's, "You are useress to me, Arec Bardwin!"
George Clooney said that he would have been insulted had he not been included in the film.
In fact, the only one of the film's targets who seems to have taken it personally is Sean Penn, who wrote Parker and Stone a very angry letter (telling them just how angry he was) after the film's release.
Dude, Not Funny!: The film had a slow opening weekend in America because people of all political stripes assumed they were the target of the lampoon. And they were right (since Matt and Trey consider nearly everyone to be Acceptable Targets). Right-wingers object to being portrayed as dicks, and walked out in the beginning. Left-wingers object to being portrayed as pussies, and walked out in the middle. Even some apolitical critics thought the film's philosophy was too nihilistic to be meaningful or enjoyable.
Harsher in Hindsight: Watching Alec Baldwin say "Good going FAG" doesn't seem quite as funny after 2013 when the real Alec Baldwin developed a reputation for saying things that could be interpreted as homophobic.
Also, Kim Jong-Il's death is finally starting to make sense, but the only difference is that it's just too bad that American dicks never fucked that asshole to begin with.
The main character's name is Gary Johnston. Eight years later, the Libertarian Presidential candidate was named Gary Johnson. Seeing how the filmmakers are known for their Libertarian viewpoints, they more than likely voted for a guy who almost had the exact same name as one of their own characters.
MATT DAMON! The real Matt Damon has said he gets this constantly.
English DJ Scott Mills actually adopted this into his show, and listeners who had never seen the film thought he came up with it. When Chris Moyles (who presents a different show on the same station) was discussing a Matt Damon movie shortly afterwards, they referenced the joke, and people texted in accusing him of stealing the joke from Mills. Moyles remarked that the joke was from Team America and pointed out that the film was several years old at that point).
I'm so ronery.
This has gone full-on to the point of becoming its own slang, with "ronery" being a term used to describe people who are antisocial jerks who then wonder why no one likes them.