All signs are that both are very special children with very special abilities:

Walt is described by his step-father to Michael as "being weird" or "creepy" or something like that. I can't remember exactly. There is a scene where Walt is studying the birds of Australia and trying to show off his knowledge to his mother and step-father, who ignore him because they are talking about her new illness, which seems to be serious already. Walt is pissed off, the same bird he is studying miraculously falls dead on their windowsill. Near the end of Season 2 Ben says to Jack, "They'll [the Others will] never give you Walt!"--like he's obviously super important to them.

Claire is told by the psychic that her baby is special and needs to be raised only by her otherwise terrrible things will happen. (It will grow up to be some kind of supervillian? Or at least some creepy badguy like Ben? Who knows?)

a.) Does anyone out there have theories on a connection between the 2?
b.) And what is the literal and Biblical significance of the name Aaron?
c.) Could there be a Walt Whitman reference going on? (Maybe Walt is the long missing gay character on the show--ha!)
d.) Possibly Alexandra (Rousseau's daughter...and maybe Ben's biological daughter too???) has some weird powers/importance too, as she is the only other surviving child to grow up on the island that we know about so far.

Just throwing things out there to see what sticks...