Mr. Woodhouse is certainly not "demented"--a word that means someone is "insane...out of one's mind". He knows exactly who he is, and is in complete mental touch with his family, friends, and environment.

I also think that much of the central theme to Emma is the idea of class/social position. Mr. Knightly presents as someone on the edge of a new way of thinking--judging a person by their character and worth, rather than the social position they were born to. Perhaps JA is setting Emma up as someone who is just being introduced to the new order...someone who must come to grips with the reality that the world, and its established order, is undergoing a shift.