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", which has an African drum solo.
"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. This and the above BLAM moments were the result of the album starting off as each band member contributing 30 second snippets and then stringing them together after the fact.
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.
Epileptic Trees: The band made it entirely clear that the plot of American Idiot is not important and they allowed fans to decipher and decide what the album's story line is in their view. The result? Numerous theories about the damn story, the most popular being whether St. Jimmy or JOS are two different people or if St. Jimmy is an alter ego for JOS. While the limited edition hardcover of the album did help this kinda, it unfortunately lead to the musical with complicated matters more. And that's not even getting to whether or not 21st Century Breakdown even connects to the plot.
Give me a long kiss goodnight And everything will be alright Tell me, Jimmy, I won't feel a thing So give me Novacaine
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.
Sequel Displacement: To anyone born around Kerplunk's release or later, you probably thought they were a new band for a while and this was their first album. The four-year gap from Warning probably didn't help. Although those people are at least familiar enough with "Good Riddance".
The plot is essentially Fight Club in rock opera form.
American Idiot itself also contains many similar themes to The Wall, albeit done from a post-9/11 and American point of view, rather than a post-World War II and British one.
"Bang Bang" from the Revolution Radio album resembles "St. Jimmy" both musically and in the way the lyrics are sung by a narrator who resembles the St. Jimmy persona.
"Boulevard of Broken Dreams" is uncomfortably close (a mere half-step down) to Oasis' most famous hit "Wonderwall". At least one mashup between the two exists, and Noel Gallagher complained, saying he at least plagiarizes from dead people, which must come as news to Stevie Wonder, who got a co-writing credit added to an Oasis B-side for obvious plagiarism. Not to mention Neil Innes, who is now co-credited as a writer for "Whatever".
"II. City of the Damned" also sounds a lot like "Summer of '69" by Bryan Adams.
And "V. Tales of Another Broken Home" sounds a lot like "Ring of Fire" by Johnny Cash.
Tear Jerker: "Wake Me Up When September Ends" is a tear-jerker when you know what it's about: the death of Billie Armstrong's dad. Though, some find it as such because they think it's about the 9/11 terrorist attack on the Twin Towers.
The title track captures a lot of the despair many young left-wingers felt at the seeming invincibility of the Republicans and George W. Bush in the '00s.
This has lessened after the election of Donald Trump resulted in similar feelings amongst left-wingers young and old in the late 2010s, creating a bit of Values Resonance for those so politically inclined.
"Homecoming" mentions Spike TV. Spike abandoned the TV in its name in 2006, and it was rebranded as the Paramount Network in 2018.
Win Back the Crowd: After the middling reception of Warning:, American Idiot brought the band back to the spotlight, becoming the 2nd-best selling album of their career and receiving very positive reviews from critics.