Only issue I have with the mouth, is its rigged inaccurately. The jaw actually is hinged and rotates open. You have it translating down to open, something used in the Mummy movies for that "huge open mouth" look.

Odds are, your centerpoint is fine. Try using the rotation instead of just translation.. the results might be more what you were shooting for.

You can keep the translation for exaggerated effects, like in the mummy movies.

Way too many people take way too many things way too seriously.