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.
Big Lipped Alligator Moment: 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.
If you read the liner, however, it works in that hearing about how (relatively) well Tunny is doing inspires JOS to pull himself together.
The very beginning of "Extraordinary Girl."
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.
"Wake Me Up When September Ends" doesn't really fit with the album's overall narrative. The song was written about the death of Billie Joe Armstrong's father.
Broken Base: Something like half of Green Day's fanbase regard American Idiot as their Magnum Opus, and the other half regard it as the point where the band Jumped the Shark. To say it's a controversial album is an understatement.
Epic Riff: "Holiday". "Boulevard of Broken Dreams" also has its tremolo guitar riff.