How did you make out with this problem? I am currently looking for a 545i or 550i and am looking for as much info as possible. Was it the alternator?
By the way, my wife had almost the exact same problem on her Infiniti M35x. Turned out to be a loose positive battery connector. It would work fine for a week, then the car would start bucking, all sort of lights would come on the dash and her computer/nav/stereo would reboot. Then it would work good for another couple of days.
A loose ground or connector could give you similar problems.