I just got a 325 Cic 2004 (built in 2003) with 42800 miles. Soon after driving the car off the dealer parking lot the red oil light started flickering when idle / stopped at traffic light. In other words I'm having same exact problem.
I took the car to Stevens Creek BMW in San Jose to resolve. They said oil was contaminated with moisture which caused the light to be on. They changed oil and scanned for faults but didn't find any.
Light stopped coming for 3 days and came back on in same conditions when idle / stopped in traffic basically when engine idle.
Have you fixed your problem?