The only one candidate I'm really not interested in for Joker is Law. I don't know why, I have just never liked him.
I think Sam Rockwell would be interesting, IF he could get over the nice guy side of him. Everything I have seen him in he always seems very non-threatening , even when he is a bad guy (this is actually the only worry I had about Depp as Joker too). Hulme I have seen almost nothing of so I can't really tell, Weaving would be ok i think, and I still want Bettany. Overall, I like most of the "contenders" for the role and I would be satisfied with any of them.
As for the "mysterious" thing, it doesn't just mean that Joker will just be lurking in the shadows the whole time. I would actually like it if Joker was "lurking" doing a killing here and there and then made a big grand entrance at the finale. I think that is Joker's style. If this is an early Joker, then this is his coming out ball. He wants the whole world to know who the Joker is, and he wants it to be set up perfectly.