Has the Dealer performed the "Recall 03V-240: E65/66 with N62 DME Reprogramming"? The following is the situation occuring in the campaign:
BMW AG has decided that a defect, which relates to motor vehicle safety exist in certain '02 and '03 MY E65/66 vehicles equipped with N62 engine. The defect involves programming of the digital engine management control unit.
Due to a DME software error, desynchronization of Valvetronic motors for engine bank I and bank II may occur, which leads to: engine rough running, "Check Engine" light illumination, misfire faults, and finally engine stalling.
There should be a round sticker located on the B Pillar of the driver door frame indicating this recall campaign was pefromed on your vehicle. If this has not been performed on your vehicle please start by having the DME updated to the latest version per the BMW "SI B12 07 03"