During tight, slow speed turning, a rubbing noise can sometimes be heard from the rear of the car. This noise is likely coming from the clutches in the limited slip differential. If the noise persists, the differential fluid can be replaced with a special oil available from BMW. On higher mileage vehicles, this noise may never be eliminated unless the differential is replaced.
Problems for specific BMW M3 years:
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Repairpal verified 2001 BMW M3 problems
The blower final stage fan resistor is known to fail. Symptoms are the heater fan speed varies regardless of the setting, the fan will not turn off when the car is switched off, or the fan will not switch on at all.