Two-Face was awesome. The look, the arc, the performance from Echart. It TIES with Ledger's Joker as my favorite thing about this movie. The look was horrifying and nasty (that gets a gasp when you first see it on opening night from the entire audience), but not so much that you look away to avoid puking. It is gross and ghastily, but not stomach churning so.
As for the look, well the idea of Two-Face is silly. The man would get infections all over that open wound if it hasn't been fixed (which they would do without his permissiion after they realized he was insane) and die within a matter of days. And you're right he wouldn't be able to talk and his left eye would go blind within hours and shrivel up in days as well.
BUT THIS IS A COMIC BOOOK MOVIE. Nolan did not intend this to be real life or taken as something that can happen, he just grounds it in so much realism and reality you accept the fantastical things as possible in a setting that is our world. Because the Joker and especially Batman re pretty unrealistic too.