From a previous post about this:
*I'm not the original author*
"I had the same problem in my E60. It seems to be such a common problem with most recent BMWs that a solution is even listed on the Auto Data automotive information application used by a large number of indy mechanics.
The problem is as most are saying here - the input flange to the differential. Basically it connects the prop shaft to the differential. the splines develop play which give the "clunk sound you are all hearing upon pulling off / reversing or feathering the throttle in traffic or over speed bumps etc.
I have a mechanic friend who did the work for me. Its not a tough job, but it is time consuming and ideally you need a car lift to do the work comfortably.
The task involves the following;
1.) removal of all underbody covers
2.) removal of exhaust from after first muffler
3.) removal of aluminium heat shields
4.) removal of prop shaft
5.) removal of differential input flange (30mm socket required). Make sure you mark the nut clearly and count the number of turns as it has to go back to exactly the same position to retain diff balancing)
6.) apply Loctiti 660 retaining compound to the flange.
7.) put everything back the same way it was removed and wait a couple of hours for the compound to dry."