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I think he's dead. I think if he was alive we would have had Wayne and Gordon commenting on how he'd need to be kept hidden away from everyone, or something. There would have been SOME concern about it on-screen.
Also, I think it was established earlier in the movie that Batman can take moderate-height falls better than other people can, specifically when he dropped Sal off the building.
On the flipside, Two-Face is one of Batman's greatest nemeses; really only The Joker is a bigger deal. And as Miriel said, they sure as heck ain't recasting The Joker until they make some new Batman movies twenty or thirty years from now.
But I still think he's dead, to be honest.
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There's a rumour that Johnny Depp will be playing the Riddler in the new movie.
Just Google it. xP I don't know what counts as a reliable entertainment news site.
I don't know about The Riddler. He's kind of... dumb. Leaving clues on purpose and stuff. That doesn't really seem to fit with the new movies. :P
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Johnny Depp as Riddler and Philip Seymour Hoffman as Penguin. But yeah, definitely just gossip and I doubt it's anything more than that.
Re: the dead or not debate...
I kinda doubt that people would be questioning Dent's death so much if Ledger hadn't died. If you concentrate on the movie alone and not think about the whole business of the 3rd film, Harvey Dent's story is kind of complete. Character starts off nice and optimistic. Tragedy strikes. Turns all vengeful and murderous. Gets taken out before he does something truly horrific. Ta da. Complete rise and fall.
I really did not get a, "...but wait! There's more!" feeling with Dent's story by the end of the film. It was done (and so well done, too).