This is Gotham. WHAT justice system.
Like I keep saying, no one needs to be framed actually. Just erase whatever evidence there might be leading to Dent, and say "case unsolved." In real life, most murders are NOT solved. This isn't a strange thing to have happen, especially in all the chaos Gotham just went through... maybe evidence was lost, misplaced, the scene wasn't sealed correctly, etc. And therefore you can't actually blame or take anyone to trial.
The best logical solution is to destroy evidence which links the murders to Dent and say nothing at all - that way they can have their cake (Dent still remembered as a hero) and eat it too (Batman can continue to help wipe out crime, without worrying about the cops on his tail and freaked out citizens.)
I know for thematic purposes Batman had to fall. I just think he should have fallen in a different way... or in a more logical way.
Haven't they heard of Occams Razor?