Mine Moment has been having BT issues as well with a BlueAnt headset. I think I have found a solution that for me at least works every time now:
First turn on the headset or BT device.
Second, go into the Moment's Wireless screen and turn on Bluetooth (if it's already on, skip this step)
Third, tap Bluetooth Settings and enter that menu. Your device should say "paired but not connected" Tap the device name then IMMEDIATELY tap "Scan for Devices"
It should immediately pair up and say something like "connected to phone audio"
An alternate thing to try is tapping the "Scan for Devices" first and then IMMEDIATELY tapping the device name.
For me, this is working 100% of the time and it takes a lot longer to explain how to do it than to actually do it, so it's not that big of a deal for me. What matters to me as that this works.
Is it as easy as it should be? No. I guess it still needs to be fixed.
Hope this helps someone. YMMV and all that.