One problem related to engine burning oil has been reported for the 2013 BMW 328. The most recently reported issues are listed below.
The contact owns a 2013 BMW 328i. While driving 65 mph, the vehicle independently drifted from side to side. The vehicle was taken to a dealer where it was diagnosed that the wheels needed to be aligned; however, the failure recurred. The vehicle was taken back to the dealer where it was determined that the vehicle was functioning as designed. The vehicle was taken back to the dealer a third time, but the failure was not diagnosed or repaired. The vehicle had previously been serviced per NHTSA campaign number: 13v454000 (service brakes, hydraulic). While driving at an unknown speed, the contact noticed a burning oil odor and noticed smoke coming from the vehicle. The contact drove home and discovered that the vehicle had an oil leak. The vehicle was taken to a dealer where it was diagnosed that the vacuum pump failed, was leaking, and needed to be replaced. The vehicle was not repaired. The manufacturer was made aware of the failure and stated that the VIN was not included in a recall. The approximate failure mileage was 45,000.