I won't go into the realism of Two-Face in a movie where the lead character wears black spandex and drives around city streets in a tank. In a real world I'd think we'd have a homeland security issue
Ah, but he doesn't! Spandex wouldn't make sense, but an experimental suit of body armor...
Nolan said from the beginning that he wanted more realism from Batman. That's why you had R'as al Ghul, but no Lazarus pit. Why you had Joker but no selective skin/hair color changes.
But are those inconsistencies? I don't recall a point in the movie that was inconsistent with any other parts of the movie.
The biggest inconsistency is in how the "realism brush" was applied.
Realism doesn't mean 100% accurate to real life. It just means minimizing your suspension of disbelief. Most people don't know the science of how speech works and won't expect a mouth with only half the lips to have speech problems. Just like the eyeball issue you have is one that no one will really pay attention to for the same reason no one cares that Joker could wander through the hospital in a nurse uniform unnoticed. Two-Face was a plausible rendition of how that character could exist in our world even if he was portrayed with movie style to make the story work.