This is one of the later Vitaphone shorts--known as a "Melody Master". These later musical shorts generally were more straight forward and had simpler sets and no real story to tie it all together--just a famous band of the day doing their stuff.
In this film, we have Artie Shaw and his band playing a swing songs. The best of these, by far, was the band's great rendition of "Lady Be Good". While I've heard this song quite a few times, Shaw and his band really did a great job by speeding up the song and giving a nice swing rhythm to the piece. You can't help but want to move when you hear it--and the music would be excellent for jitterbugging...though I think there are only about 15 people alive today who can jitterbug! I know I can't, as it takes the athleticism of a track star to do it well! And, although the young adults do pretty good, in the late 30s and early 40s, there were some dancers who would have truly amazed you with their huge leaps and tosses.
By the way, this has nothing directly to do with the film, but when I watched Artie Shaw, I just couldn't understand his allure to women. He was married eight times (wow)--including marriages to Ava Gardner and Lana Turner.