Personally, my second cousin was in the movie :) He was flipping the bird and screaming at the Nazi's on the bridge!
Here are a few drum related discrepancies:
Taken from IMDB
When the band is playing in Ray's Music Exchange, and also at big gig at the end, we can clearly hear the drums and cymbals crashing, but the drummer is faking his movements; the cymbals do not move, nor does the drummer actually make contact with the drums with his drumsticks.
The music played in the church does not coincide with the musician's movements, especially the drummer; the soundtrack plays the snare drum while the depicted drummer is on the upbeat, and not the downbeat.
During the big concert at the end, when Jake and Elwood are being introduced, it's obvious that Willie is not hitting the cymbal and is, instead, playing air drums.
When Elwood hits the drum store in the mall, there are no drums on the Bluesmobile, but a couple of shots later when he starts fleeing they're now on top of the Bluesmobile.
When the band is playing "Jailhouse Rock" at the very end, the drummer goes from hitting the ride cymbal to the high hats in the same bar (four measures).