One problem related to ignition has been reported for the 2003 BMW 325. The most recently reported issues are listed below.
Xenon lights went out shortly after the 50,000 mark. Shortly after car kept going into fail safe mode, kept getting low voltage readings on diagnostics. One BMW dealers kept telling me I needed to rebuild transmission. All they would do is plug the car into the computer and see the tranny reading on the scanner. The reason there was a tranny reading was because the car was in fail safe mode. I eventually had the tranny rebuilt and I still had the same issue. I would cycle the ignition and restart the car and car would drive fine. It keeps going into fail safe mode everytime I start the car. Its harder to get it out of fail safe mode in the winter with colder starts.