Happens on our CPO 2006 325i and has been a major pet peeve from day one, at least for me. Dealer says they can't raise the idle, so I'm stuck with my right foot on the throttle to keep the revs up.
The vibration is irritating. It's fine for the first 5 seconds when you stop, then the revs drop to 648-650rpm and the whole car vibrations. Seats, headrest, steering wheel........annoying for a BMW. I figured it was the design to save fuel combined with perhaps something just being a bit out of the normal tolerance levels.