I also am experiencing issues with my Moto X and bluetooth. Something tells me it is due to the custom bluetooth 4.0 implementation that Motorola used for Android 4.2.2. I figure that the only "real" fix will be waiting for the 4.3 OTA to add official support.
I tried everything under the sun to resolve my issues. I did a factory reset, un-paired and re-paired, tested on multiple devices and even did a RMA with Verizon. I called up Motorola prior to the RMA and told them about the issue and they said that it was a defective unit. I'm planning on calling them again today to let them know they have an actual issue with at the very least the verizon moto x.