One problem related to differential unit has been reported for the 2008 BMW M3. The most recently reported issues are listed below.
M3 with dct automated manual transmission will not shift when at lower speeds going around corners. There is a long delay before it shifts so its dangerous when merging out into traffic. The car has performed this way since purchased and multiple software reprogramming has not remedied. When turning the rear differential makes a grinding noise. It started at about 1200 miles and continues at 5000 miles. The dealer put fluid in to remedy and said to wait 300-500 miles for it to go away. That was over 1500 miles ago. . . . . . . . . . . . . . . . .