One problem related to automatic transmission has been reported for the 2002 BMW 540. The most recently reported issues are listed below.
On 7/19/2008, my 2002 BMW 540i with automatic transmission caught fire while myself and my wife driving toward an evening party. At first I smell something is burning then see a tiny bit of smoke. I parked the car in a bank of America parking lot and my wife went out to check the car, and she saw fire started to burst. We call 911 and within five minutes, the front end of the car is in flame. The local fire department came the put out the fire. The car is now been tow to a local shop and will be moved to the "total lot" of my insurance company. I did a quick search on the internet, and found out I am not the only one. I hope BMW can find out exactly what cause the fire and fix the problem. My wife and I are lucky since we got out of car soon enough. This is not a good example for BMW such a luxury brand. Sincerely, steve hung.