There are some deep things going on here. Defense attorneys for villains are typically caricatured as contemptible, sweaty little men who try to bluster through their cases while tugging nervously at their collars. This shows the other side of things - yes, the Joker is a monster, but he's still a person, and the people defending him are just doing their jobs as the law requires. Even the bad guys deserve representation, and the lawyers who take on that task get spat on and booed for their efforts. It's a tricky issue, and handled well here.
I agree, this is an interesting take on Harvey's final fall from grace. As in all the best Two-Face origins, the scarring of his face is almost an ancillary concern. Where the seeds were REALLY planted is with that 'after all'. Up until then, he was, for all his flaws, a scrupulously honest man, and shocked that he had almost been duped into crossing the line. SO shocked, in fact, that he's willing to take ANY methods to bring the Joker down. 'After all, it IS the Joker'.
It's that 'after all' that brings him down. Until then so rigorous a champion of laws and legalities, he starts to fight dirty - and when he starts, he can't stop. Because this is Harvey Dent here, a creature of extremes - he devotes himself whole-heartedly to whatever he's doing, so when he crosses the line, he crosses it HARD. And yet, for all that, he is still primarily a good man trying to do a good thing, and it is the actions of a good man - taking the acid in place of his wife - that dooms him.
Also, it's interesting that it is a random member of the public that does the scarring - the public that he was trying to defend the interests of. And through an accident. Through FATE. The 'innocent' tries to punish 'the guilty', and winds up disfiguring the innocent's defender purely through circumstance. If that's not a portentous beginning to his criminal career, I don't know what is.