Lyric discussion by rwiggum 

Cover art for Beautiful Mistake lyrics by New Amsterdams, The

Actually, I disagree. I think this is written about Matt's time with The Get Up Kids. See, look at the first verse. In an interview in AP magazine during their farewell tour, they told a story about their first tour ever. Jim drove the van over a pothole and broke the manifold, so it started pumping fumes into the van. They had to drive from Kansas City to Chicago with the windows down (hence the "Breathe broken manifold") line. Then "part of my history" line, that's pretty obvious.

Then in the next verse, the line of "Long days full of bad notes" likely refers to when the band was first getting started

Then, at the end he says "I see clearly now, I never will escape. Once we took the time to make a beautiful mistake." I think that's the central theme of the entire song, which is to say that he's afraid that his long legacy as The Get Up Kids' frontman will overshadow any future endeavors, including The New Amsterdams, but he doesn't regret that time. Hence, "The Beautiful Mistake."