Can the mouth move without sound?

Certain mouth shapes will be activated based on facial recognition (smile, for instance), but if you see the mouth randomly moving while your microphone is enabled but you're not talking, and you DON'T see those movements when you disable the microphone, then it's noise is likely being picked up and causing those mouth shapes. You can go to Edit > Preferences > Lip Sync and change the "Audio-based Muting" parameter from the default of "-36 dB" to something lower.