I have had all manner of Bluetooth problems lately on my 920. Tried using it with the Jawbone Jambox, my Sony stereo BT headset, and my VW GTI (2010) car stereo unit, and all three exhibit problems differently.
The first time I connected it to my car it only did a music connection, so when a text message came (I have the read-aloud ease of access on) it would announce through the car audio just fine, but fail to use the car's microphone so any attempt to dictate a message resulted in it not being able to pick up any sound, as it was in my pocket. When getting in and out of the car it would only auto-connect half the time, whereas my old iphone 3GS never failed. Sometimes it would get both music and voice through to the car, sometimes just music, sometimes none.
Tested this similarly with the Jawbone Jambox. At first it worked perfectly but then a day later it was only doing voice and not music. Doing a cold reboot and deleting / re-pairing the device finally got it to see both protocols again. A similar thing also occurs with my Sony stereo headset (IS-800) so this is definitely a problem with wp8/920 firmware.
Very frustrating, not being able to predict what successfully connects, and having no assurance that it automatically sees previous devices with the same settings. Anyway, just wanted to share my experiences. It seems this issue is quite widespread, any word on when a fix is coming?