I was having the same issue on my E46 M3 Diff. Sounds like you are dragging something under the car.
I had the rear diff fluid changed with their latest Diff Fluid w/FM Booster, Part# 8 22 2 282 583 and the noise has gone away for now.
It is amazing to me that the new M3 is having the same issue. You would think BMW would eliminate such annoying noise.
PS> the dealer recommened the wrong part number! I had to correct them based on input from this forum