In the first season Hurley told Jack that his name wasn't Hurley, that that was just a nickname that he's called. "Why? I'm not tellin'." That particular swali has always pestered me and to my knowledge has not been answered. I'd be fine if that was the only thing unanswered. LOL.
I don't think the writers are going to answer where the woman in blue came from. I'm ok with not knowing, but I will admit I'm a bit curious.
Also, if Claire wasn't the one that told Kate not to bring Aaron back to the island, then who did? MIB can't leave the island. Why did that person tell her not to bring Aaron back? I don't think I'll get an answer to these maswali either.