I am having the same problem. Tried many ROMs (Cyanogenmod, Jellybam, Omnirom, Revolt,...) but anything above 4.1.2 leads to this strange issue. At first i thought it was the Bluetooth device thats why I tried several of those as well (Plantronics, LG, Samsung, Bose,...) and its the same every time.
I really can't get behind this and never found anypne with a simillar issue. I have pretty much resigned myself to always having 4.1.2 until i've seen this thread. Now i have hope, please don't crush it.