In the comics, Bruce's body doesn't degrade.
A. Obviously his body wasn't degraded enough to prevent him from being somewhat effective as Batman.
B. It most certainly does. Does it degrade due to a single incident or between films? No.
But he's constantly getting injured, piecing himself back together, and having to deal with the physical and mental consequences of his crusade.
Regarding the coverup:
Yes, Gordon is suffering internally. The problem with the whole execution of the idea is that it starts there, and he's already there, and then it never goes anywhere. He never really changes as a character in any sense. Far as I can tell, the coverup has no appreciable impact whatsoever on the people of Gotham. They don't question what they know, or what they've been told, they never have to deal with the fact that their White Knight became a madman (an inifnitely more interesting and powerful concept, its kind of half the point of Two-Face) they're no more inspired than they would otherwise would have been...its just...nothing.
It feels like a Jerry Springer episode. His lie is revealed, but not becaue Gordon had finally decided to come clean. And then he tells Blake that there's a reason he lied...which we already knew to begin with. Blake calls him on what he's done, he only real interesting idea in TDKR regarding the "lie", and instead of exploring the morality of it at all, its basically just an excuse for Gordon to make an overdramatic speech to inspire Blake...a speech which Gordon could easily have made without the lie in the first place, because duh, Batman operates outside the law. The idea of breaking the rules to seek true justice isn't new to the franchise, nor is it particular interesting just because Gary Oldman is shouting about it.
In the end, the message about "Sometimes people deserve more than the truth" (which is nonsense) and the message about "The rules can sometimes limit you" get mixed up and muddled, and both suffert for it. Its all just kind of haphazardly handled.