Mickey and Mitch performing "A Kiss at the End of the Rainbow" near the end, for the first time in years. What's especially touching is how the other characters gather round backstage to listen.
And then, of course, all of the musicians together performing "A Mighty Wind". They might not necessarily like each other, but goddammit they can all be united by great music.
The Mitch and Mickey song "The Ballad of Bobby and June" from the soundtrack. A classic-style lovers-separated-by-war song. However, unlike most songs of this style, Bobby does manage to get back home unscathed.