Yes, I mean that if the burn was deep enough to burn all the way too the skull, there would be no muscle, tendons or nerves able to move it, and Two face would have lockjaw all the time.
I faced that same predicament when I sculpted mine, was careful to leave enough meat on the bone.
And the eyeball gave me the same Hell, that was until I looked up acid burn victim pics and saw a good shot of an eyeball. So I know it could survive the acid. Don't know much about how much vision he would have. But he could keep the eye.
Another snag was Hair. I never did like that in the comics and cartoon, they had his hair all grey and crazy on his burned side. I mean, if the acid burned through the skin, the hair follicles would go bye bye as well. They would probably go first. Anyone who has ever been burned knows that all too well.
But, I tend to overthink things.