Edward,
To answer your first question, no not all LG phones have a problem. MY LGL22C running Android 5 has no problems connecting to the meter.

But I suspect that info doesn’t really help you much. I will say I have noticed at least one other person in this forum who has/had problem connecting with the Moto G. I don’t know final resolution, but here is a summary of the easy stuff you might try based on various posts from James and others in this forum.

1. In the phone, turn airplane mode off then on. Sometimes that is enough.
2. Reboot the phone. Sometimes that is enough.
3. In the phone, go to Settings->Bluetooth->Paired Devices. If the Mooshimeter is listed under paired devices, delete it.
4. Open the case (2 screws) and press the tiny reset button (near the microSD card slot). This reboots the meter.
5. Remove the 2 batteries and check their voltage with another meter and replace if low. Some people have had low/dead batteries even if they haven’t used the meter much.
6. Sometimes the meter thinks it is still in shipping mode, so momentarily short the meter probes between ohm and common. (This is not likely).
7. Uninstall and reinstall the Mooshimeter app.

If none of those work, then you might post the phone android version, the meter app version, and meter firmware version, which may spark a better solution from someone here. If you have success, post the solution here for the benefit of other folks who might run into this problem.
– – – Duane