I also went to Letterman not that long ago. The band plays a lot, they're really great - it'w worth it for the band alone. When you first get there, some people came out and gave the ground rules, then a comedian/intern/whatever came out and did like a warm-up, where we all practiced how great we could clap/yell/respond/laugh. Then Dave came out for about 3 minutes and talked to somebody down in the front row, and then they started taping and Dave did this thing with the guy he talked to in the audience like it was an old buddy or something.
During the commercials Dave just sat there talking to an assistant. The guest (some movie star lady, I forget who) had people come out and do makeup & hair - very funny. I forget who the musical guest was, but they did their act twice. I couldn't tell the difference, it wasn't like they messed up or anything. They just did it once, and then repeated the whole thing.
It was interesting how Dave just kind of sat there, and then when the camera turned on he changed all of a sudden into his TV personality. The lights come on and the signs say "Applause" and somebody stands in front of the audience and waves for more noise.
In the middle of the taping, they came out and said that they were also taping a special thing for use at a private sports affair, and they wanted us to cheer every time Dave said a bunch of names (which I never heard of, so obviously it wasn't baseball, the only sport I follow). So Dave said names and we cheered.
It was fun.