The WOT, wide open throttle, bypasses the AFM, air flow meter, and allows the fuel injector pulse to go to the maximum.
That would explain the issue you are seeing so the answer is the AFM, requires adjustment.
You can test by manually moving the flapper door to see if it makes the engine run better.
You can test this by measuring the output of the o2 sensor at the diagnostic plug on pin 15.
o2 sensor readings.
You can check it on your diagnostic plug though.
Use a VOM on pin 15.
.6 volts is dang rich .3 volts is dang lean.
http://www.kemparts.com/TechTalk/tt07.asp
http://www.unofficialbmw.com/images/reset1.gif
1. Ground
4. Temperature sensor
7. Reset
8. TDC sensor yellow
9. TDC sensor shield
10.TDC sensor black
11.Start signal
12.Alternator charging excitation voltage
13.Ignition coil
14.Alternator charging supply current
15.Oxygen sensor output to test with.
Later,