You'd think the whole "Batman killed cops" thing would've struck people as odd and out of character for the vigilante who worked to "help" the police for a year.
The final montage-like scene over the end of the movie is one of my favorite moments. Gordon's V.O. intercut with Dent's public funeral service, Batman fleeing the police, the aforementioned scene with the spot-light. It's very well done and it'll be interesting to see how in the next movie Batman gets back in Gotham's good graces.
But there was just something about that scene with setting Batman up as the "Dark Knight" was just powerful and awesome.