The Dark Knight trilogy really wanted to be a realistic, grounded take on the Batman mythos, so they dropped the more fantastical elements of some characters' backstories. Ra's Al Ghul was no longer immortal, Bane didn't have super steroids, the Joker wasn't permanently bleached by chemicals...then there's Two-Face.
I guess they thought acid burns were too unrealistic, so they gave him regular burns...apparently without knowing that burns that severe would be so painful that he wouldn't even be able to remain conscious, much less run around the city on a killing spree. I mean, you can see exposed muscle in some places. There's a line where Gordon says he's rejecting skin grafts, and I remember thinking, "WTF are you talking about? He should be in a medically induced coma, not making healthcare decisions." Half of his body was an open wound; I'm amazed he didn't die of infection 15 minutes after he left the hospital.
He should have also lost the one eye, like if your eye lids were burnt off there is going to be definite damage to the eye itself. Looked fuckin’ rad though so he’s got that going for him.
There was an analysis of Nolan and post-Nolan Batman that argued that once you strip away all the fantastic parts of Batman, all the Clayfaces and Mr. Freezes and Poison Ivies and the sentient robots and uncanny weirdness, all that is left is a bunch of problems that frankly the cops should be able to handle, and that Batman at that point is just a cop who is willing to violate people's Constitutional rights.
If Batman can be replaced by a well-outfitted SWAT team, then you're not writing Batman well enough. Give him some insane nonsense that cops are not equipped to handle.