Well I'm not an expert but since no one else has responded I figured I'd at least give the thread a bump.
It can be almost anything from the fuel and air filters, to bad spark plugs, or valves needing adjustment. Check what maintenance has been done recently. I personally don't have any experience with the 316i so I don't know any of it's quirks. Also is the engine rpm dropping past normal rpm down to 650-700? And does it only vibrate when it reaches 650 or does it vibrate all the way back to normal rpm?
Also I believe your bmw has an onboard diagnostic system that you can use. This link should explain it for you. http://www.pelicanparts.com/BMW/tech...nostics%20.htm
This might help narrow it down.