One problem related to headlights has been reported for the 2002 BMW 540. The most recently reported issues are listed below.
The plastic covers on on the headlights of my BMW became crazed/frosted. Every BMW of this vintage has the same problem. I showed this to occur in 2010 at 100,000 miles, but in fact it was a steady degradation over several years. It's a safety issue, because the light output is significantly reduced. Causing risk at normal highway speeds. In addition, the crazing/frosting results in additional glare to oncoming traffic. I asked about recalls/replacement program for this defect at my local BMW dealer; the service technician dismissed it as a normal aging issue. I strongly disagree. A car of this price, or any price, should have headlights that last longer than a few years. I'd replace the headlamp covers if they were available, but the only solution is to replace the entire headlamp assembly at a cost of $1238 for each side. Yes, $1238. This was a quite expensive auto, but regardless of cost, this safety issue should result in a recall.