Hi Kalphablue,
That's a nice piece
Depending on the aim, you may keep this 'rigid' way of animating to give this funfair feeling.
But if you want to animate a character with volume, you should think in term of skull and muscles.
Moreover, you should try to animate as many part as possible to give a full motion to his face.
I did a quick edit so you can see what i'm talking about :
Good luck !