Could be anything... I have a 2001 3.0I too and like you I had the engine going to stall (while idling), the DSC, ABS and brake warning lights coming on, then the SES light and even the limp mode. Connected my code reader (Peake), it displayed several codes, mostly related to misfires and 02 sensors misreading, and also revealing several times a problem with the throttle body. The problem occured many times during the following days, while I was waiting for the delivery of the new throttle body (and MAF and O2 sensors while I'm at it).
It was interesting to notice that the problem occured less and less often, and when the SES light went on, the scanner just displayed codes related to misfires, no more throttle body failure... Then, just when the parts arrived in my mail box, problem completely disappeared! The engine now idles very well, runs smooth, no more warning light, running fine just like before...
So what happened? Maybe some bad electrical connexion, some dust or water around a sensor or in the idle valve, or in the throttle body... Just to tell you that the warning lights seen on the cluster or the codes read by the scanners don't always tell you exactly what is the real cause unless you have at home the very expensive BMW diagnose tool...