Since you posted drawing of the rear Im guessing he at least told you the problem is with the rear setup.
Ask if the rear trailing arm bushings (#4 in your pic) are worn out (RTABs). This is the most likely culprit. If so they have to be replaced.
If you have some mech ability and the proper tools (Search DIY RTAB here or on the E46 Fanatic forum) this is not impossible to do yourself - but if not... its gotta get done.
http://www.zpost.com/forums/showthread.php?t=673800
Unless you track or just want the car much tighter (and rougher) I'd go with a rubber bushing
Parts:
ECS :
http://www.ecstuning.com/BMW-Z4-3.0i...g_Arm/ES57714/
or
http://www.vorshlag.com/product_info...products_id=59
Good Luck