This sounds a lot like the issue:
This Service Information bulletin supersedes SI B33 01 02 dated February 2008.
Grinding Noise from the Differential during Slow Cornering
E46 M3 from start of production
E60 M5 from start of production
E63, E64 M6 from start of production
E90, E92 and E93 M3 from start of production
A grinding noise may be heard coming from the differential during slow cornering.
This noise is best heard during tight cornering situations.
For example : while parallel parking, driving in a tight circle, etc.
When the rear wheel speed differential varies during tight cornering, a slip stick effect is created on the lining and steel discs incorporated in the differential locking clutch, causing the grinding noise.
This noise typically goes away as the locking clutch discs in the differential are broken in.
The break-in time varies depending on driving habits.
For example : tighter cornering (working the locking clutch) means that it takes less time to break in the locking clutch discs.
If a complaint is verified as described above on the E46 M3; E60 M5; E63 and E64 M6; or on the E90, E92 and E93 M3 vehicles, the differential oil should be replaced with a specially formulated differential oil, BMW part number 83 22 2 282 583.
Road test the vehicle. (the part I hate the most and every other technician.perhaps most of them skip this part.I would rather give you the option to perform this or at least inform you of this procedure.)
With the vehicle at operating temperature
Drive in tight circles (20 circles in each direction), allowing the special oil to coat the locking clutch discs.
The grinding noise will decrease when the locking clutch discs are sufficiently coated. Some slight noises may still be heard after driving in tight circles. Its necessary to drive the vehicle up to 600 miles before all noises are eliminated as stated by the manufacturer.
Note: Vehicles that have had the differential oil converted to this special oil should continue to use this oil whenever a service requiring the differential oil replacement is indicated.