It's not the car, it is something with the Samsung BT stack.
While I have no issues with the output being stereo, neither the GS III, Note 1 or Note 2 will maintain a connection to the BT in my car or my wife's.
Every time I turn the car on I have to go to the BT settings, find the car, click connect. If I turn the car off, I have to repeat the procedure. It is a major inconvenience and something I have not experienced with any other phone.
Every other phone I tried it just remembers the vehicle and if I start the music player, it starts playing through the car speakers.
None of my Samsungs have ever done that.