I think they were trying hard to make it look like a split suit and have just little bits to imply the duality of him. I actually like that design choice, he looks right without having to fall into the exact details of the comics.
I agree. But I just think they really blew it on the pants. I don't expect them to be burnt when only the top of of the jacket is, but some gas stains would have helped. Again, not something you'd see in the film really, but for the costume's sake it would have made more sense.
But the burnt jacket did give that "split" look without taking a white and black suit and sewing them together. Much more realistic this way, especially if he went on a killing spree right from the hospital. He wouldn't have time to go make a custom suit and then go on his rampage