American Idiot/YMMV

Arc Words: Inevitable, given the storytelling aspect of the album, but a few stand out, especially in 'Homecoming'. Part 2 bears resemblance to the 'I don't care' part of Jesus of Suburbia, acting a bit like Book Ends as JOS returns home. Also, Whatsername's 'Nobody likes you' taunt shows up quite a bit, possibly to imply thoughts going around JOS/ Jimmy's head during the song.
Anvilicious / Some Anvils Need to Be Dropped
Audience-Alienating Premise: The band decided to make the initial tour of the album on Texas, Tennessee and Georgia. Not only they stayed far away of selling out all of the tickets, some fans who did show up booed them playing the album's songs. Making an anti George W. Bush album and then going to play it in the American South at the apex of his popularity didn't work.
Non Sequitur Scene: The "Rock and Roll Girlfriend" bit of Homecoming doesn't make sense in the album's context, and was never mentioned before or after the song. It makes more sense when you realize it's about Tre's life, but it still doesn't really fit in with the rest of the album.
- For a few years after its release, several older and more hardcore fans tried to play the entire album off as a BLAM within the band's career. As we can plainly see, It Got Worse.
Epic Riff: "Holiday"
Genre Deconstruction: Of the Punk movement as a whole. JOS becomes a self-absorbed, self-destructive rebel without a cause who ultimately accomplishes nothing and according to "Letterbomb" is the real American Idiot. This creates the interesting social commentary in that rather rather than turning people into mindless drones, the alienation and paranoia of modern American society creates self-destructive rebellion.
Germans Love David Hasselhoff: The album did quite well overseas, unsurprisingly during the time when international opinion of the US had hit rock bottom.
Ho Yay: If you consider Jimmy a separate person to JOS, there's some of this as subtext, especially in Give Me Novocaine.

Out of body and out of mind
Kiss the demons out of my dreams
I get the funny feeling that's alright

Jimmy says it's better than here.

- In the musical it gets a little more explicit - while JOS and Whatsername serenade each other, Jimmy leans mournfully over the balcony and sings to JOS,

I text a postcard, sent to you
Did it go through?
Sending all my love to you.
You are the moonlight of my life every night
Giving all my love to you

- - It could likely be interpreted as JOS' thoughts/feelings about Whatsername at the time, considering the Double Consciousness interpretation.
Tear Jerker: "Whatsername" is so very much this.
- "Boulevard of Broken Dreams" and "Wake Me Up When September Ends" also count.