One problem related to battery has been reported for the 2003 BMW 325. The most recently reported issues are listed below.
Multiple intermittent problems with door locks failing to open either by key fob, depressing button inside car, or by pulling inside door handle. To exit car, must lower windows and insert key into outside keyhole. This is a serious hazard! problem arises with no apparent cause, then will disappear a few days later with for no apparent reason. BMW replaced actuator (?) and the problem appears to have disappeared, but it cost me $1400. Other electrical problem is with air bag warning light coming on after car sits undriven for more than a couple of days. Was told that air bags will not work with light on. No reason found. Battery checks out fully charged.