One problem related to car accelerates on its own has been reported for the 2005 BMW 530. The most recently reported issues are listed below.
While driving in a parking lot at approx. 3-5 mph, my 2005 530i suddenly accelerated while my foot was on the brake. I pushed on the brake pedal as hard as possible to slow the vehicle, then quickly shifted the automatic transmission into park and turned off the key. I took the car to the BMW dealer where I bought the car. They were unable to find the problem, so they have brought in engineers from BMW north America to analyze and fix the problem.