BMW: 84 bmw running rough, external pumps, bmw dealer

Question
My son has a 1984 bmw 318i which appeared to be running fine and just needed a tune up. three days after purchasing the vehicle he started having problems. the car idles at about 1500 rpms and idles fine but if you try to give it any gas to move quickly out of the way it bogs down(acts like its flooding) we checked the spark plugs and they are black with soot(brand new plugs) Also there is a high pitched whining noise in the rear and I had my local bmw dealer take a look at the fuel pump and they tell me everythings ok. We've been going crazy trying to figure it out but so far have had no luck. the car seems to do fine if you baby it but if you need the power to get out of the way of something it fails. if you can give me any advice on what to check I would greatly appreciate it.  

Answer
Tom,
 I am not experienced as much with the 4 cylinder 318 as with the 6 cylinder models, but I will help as much as possible.
 You mentioned you have changed the spark plugs, but what about the plug wires, distributor cap, distributor rotor, and coil?  Alot of times the engine will run fine at idle but under load it will sputter or have flat spots.  I've had these same symptoms, and a tune-up (what I listed before) solved it.  Also change the fuel filter if it hasn't been done recently.
 That car should idle at about 900-1000rpm.

 The "whine" you hear from the back seat IS the fuel pump.  Some do it and some dont, I dont know why either.  My pump in my '87 has a whine like that as well.  You should have the 2-pump set up being an '84 model.  You will have a primer-pump in the tank and an external pump in front of the driver's side rear tire.  Most of the time the "whine" is due to the main pump failing and the primer-pump having to work harder.  My pump is whining, but still puts out correct fuel pressure (~30-35psi @ idle).  So if you want the whining to go away change the pump for a new one, or check the external pump and make sure it's working.  The external pumps do it too, but its more of a "whizzing" sound.
 The "soot" you are talking about is because the fuel is not being ignited under load and it is collecting on the plugs creating carbon deposits.
 In summary I would do a full tune up, plugs (stay away from the platinum-4 plugs, not worth the money) plug wires, distributor cap and rotor, and possibly a coil (they go bad too).
 If you have any more questions please let me know!
 Take care,
 Josh