I just purchased a 2003 525i with 152k on the clock.The check engine lamp would come on at traffic lights when stopped occasionally along with the transmission limp mode. The code was p0720. One other odd thing was I noticed all the lamps in the car were flickering or pulsing.
The car had a rebuilt bosh alternator that did not look very old. Upon checking the alternator with an old style analog needle type meter the charging output it was swinging low to high.
I put a digital volt meter on it and it would not pick up the rapid swing in voltage.
This had every symptom of a bad alternator. I replaced the alternator with a reman Bosch unit and it seemed to be fine. 2 days later here we go again with the check engine lamp and trans light again? Same code p0720 !
I found a loose ground cable from the battery on the rear body panel that looked good until you gave it a tug. Tightened the cabe and it has been fine ever since!