So what does it have going for it? The music, of course, and there's some great music and plenty of it. I saw this first when I was a kid playing clarinet in a high school band, and like Allen I was a nerdy guy with glasses (still am, now that I think about it). To think that a guy like that could play a clarinet the way Goodman could was a wonderful thing. Two famous concerts are represented in the movie, including the climactic one at Carnegie Hall in 1938. If you don't watch the movie, check out the CD of that concert. Great stuff.
Some famous jazz musicians show up as themselves in the film: Harry James, Kid Ory, Gene Krupa, and others. So it's a historical document, too.