BMW E90 E92 M3 Free Play Shim
Almost every E9X M3 Factory LSD units has problem withfree play in right drive shaft. That can be recognized by hearing tap sound when engaging into 1stgear and/oroil leakon right side of differential. This problem can cause further damage to your differential such as clutches and bearings premature wear due to lack of oil. So it is highly advised to solve this as soon as possible.
Gear Lab FREE PLAY DELETE SHIM will resolve this problem without any modifications. Just replace factory shim which goes behind right side gear with this shimand you will resolve that problem for good.