Many of the complaints about American Idiot are in regard to how overplayed and annoying the singles are without actually saying much about the album in general. American Idiot is not a record that can be judged by the singles.
This album was crafted as a cohesive work; it isn't meant to just be thought of as a random collection of songs. I don't have a TV and don't listen to the radio very often so I can't attest the accusation of these songs being overplayed, but I know that I ordinarily would not be able to stand a song along the lines of Boulevard of Broken Dreams. However, while listening to the album, it's the perfect song to follow Holiday, which itself is the perfect song to follow the end of Jesus of Suburbia. There is a logical, musical, and lyrical progression from one song to the next through the entire album.
I'm somewhat privileged to live in the relatively media-free bubble that I do. I don't feel the need to defend my punk rock credibility by tearing down the pop rock band that was part of the punk scene over 10 years ago, and I'm not driven to buy into the hype surrounding whatever band is popular at the moment. My opinions of this record come from my experience of taking it home and sticking it in while I was washing dishes, and being completely amazed by the quality.
Also, the fact that I, an aging punk rocker, and my roommate, a jazz musician, both think that it's the best album of 2004 should say something.