One problem related to engine belts and pulleys has been reported for the 2011 BMW 328. The most recently reported issues are listed below.
Takata recall: all began from purchase 09/2013 had engine bolt fixed on recall, but since several engine work performed due to loss of power when driving, had replaced coil/tune up done, several gaskets in the engine hasd to be replaced by BMW dealer, and dealer can't fix vehicle for "sputtering/back firing" when sitting at light or stationary it just stutters. Time to time driver window will not roll down when in car. Also, the seat belt light chimes to put seat belt on and no one is in passenger seat. Stereo lights pixels burning out & sound from time to time the speakers has muffled sound or poor quality sound. Brought car with 20,000 miles and now has 57,000 miles and issues with engine is way too much for low mileage.