on some of the earlier model that was doing this the bmw dealer use the software to bring up the rpm just a tad. then with the newer models they couldn't they told the customers that it was a know problem with no fix. i'm leaning more towards the AIC=air idle control solenoid.
why because i just did a head gasket on my 02 3.0i never had that issue.while it was apart
i clean out the AIC and the throttle body put vehicle back together and from the moment
i start it up took it for a ride bamm the idle vibration started.when i put my scanner to check rpm is fluctuating from 598 to 689 to 705.just my 2 cents