I had a pretty similar thing happen to my '81 a few weeks back. Mine was combination of 2 problems. ICU was fried and sending out random sparks and therefore causing erroneous backfiring. And the Hall effect sensor had also given up the ghost which was why mine stopped completely. As others have mentioned yours sounds like the ICU.
There are 2 diagnostic tests you can do to check the function of the ICU and the bean can.
Bean can test
1. Remove plug and ground
2. Make sure battery is disconnected, remove front cover of engine
3. Take off the bean can from the front of the camshaft. leave it plugged into wiring harness
4. Reconnect battery and turn ignition on
5. Rotate mechanism by hand and check for sparks - there should be 2 per bean can revolution.
The other test is to check the ICU is functioning properly. Carrying on from previous test
1. Disconnect battery again
2. Unplug the bean can electrical connector
3. Find a paper clip or similar conductive material and wedge it into the
[size=12]middle[/size] pin of the electrical connector (the outer two are the 12v +/- the middle is the signal wire). Find an area to ground the pin to. I used the engine casing. Whatever you do, don't use the diode board!!
4. Reconnect battery and turn ignition on.
5. periodically ground the paper clip. Every time the clip is grounded a spark should fly. If no sparks, double check the spark plugs are grounded. If still no sparks it is probably ICU. or Coil. Though it would be wise to check the outer two wires with a multimeter to make sure power is getting through.
If it is sparking when the paper clip is grounded then your hall effect sensor has died. Fix it yourself as BMW wanted to charge me nearly $800 for a new bean can and you can the sensor pretty easily for around $20.
6. Turn igniton off, disconnect battery. Replace whatever is necessary. Go for a satisfied ride to enjoy your handy work
