I just got the Xperia ZR a month ago. And I loved the 4.1.2 update that already came preloaded with it. The bluetooth, the Wifi and almost everything was working perfectly. Till I decided to upgrade it to the latest 4.3 [10.4.1.B.0.101] upgrade. A lot of people, like me, had issues with the bluetooth unable to detect other devices or be detectable to other devices. And I've seen plenty of complaints on the Sony Mobile blog/forum, too. A lot of them got their phones replaced, re-furbished, re-serviced by Sony; which didn't really solve anything. And a lot of people saying that the temporary fix was to apply loads of pressure on the NFC logo near the flash at the back of the device. Here, I'll tell you a short but permanent fix.
Open your device. Remove your Micro-Sim and SD card (if any) inside and then apply pressure on the area near, where the 'MIC 2' is written. Not much, just a little. And then insert it back. Now put your SIM and SD card back inside, and your bluetooth will work.
I guarantee you it will.