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...

I don't think Alex is Ben's biological daughter. Rousseau was pregnant when she arrived on the island with her baby's daddy Robert. That'd be cool if she did have special powers. It seems like they take any and all children though. They took Zack and Emma right away and they can't all have powers. I think they just take the children because they believe it is better for the children. Goodwin said to Ana Lucia that the children are better off now. Not sure why they haven't really tried to take Aaron. Alex wasn't very old when they took her, 2 weeks? 2 months? I would say Walt definitely has powers, not only the bird murdering thing but also he sort of teleported himself across the island to talk to Shannon. Unless that was smokey but I don't think so. And Locke says Walt is special. In the bible, Aaron is Moses's brother. Moses was afraid to speak to the Hebrews so Aaron was his spokesman. I think he was the first great high priest or something. He did rebel against Moses a little and he allowed their people to make the big golden calf (a big no-no)when Moses was up on the mountain talking to God and getting the ten commandments. Children are like sponges and are super fast learners so if the island increase brain use...there's got to be some connection there. I read a Dean Koontz book about kids with super mind powers that could do some freaky things. Walt reminds me of that book.

A little off-subject, but "special" was a word I noticed popping up often on the show:
Boone says Shannon is special (hearts and minds)
Locke's mom says Locke is special (deus ex machina)
Tom says Walt is special (the hunting party)
Mrs. Pace says Charlie is special (fire and water)
Dr. Alpert says Juliet is special (not in portland)
Ben says Locke is special (man from tallahassee)
Ms. Klugh asks Michael if Walt has special powers (3 minutes)
Psychic Malkin says Aaron is special (raised by another)
Jin promoted "special assistant" to Mr. Paik (in translation)

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Danielle's baby was 1 week old when they took her. I think Danielle was going to hurt baby Alex. That is why the Others took her, they saved her from crazy Danielle. She'd already killed her entire group because they were 'infected' and she told Clair (in Maternity Leave) 'I hope your baby isn't infected but if he is you know what must be done' That would explain why they stole Alex and not Aaron. I know they tried to get Aaron before he was born but they haven't tried again. They weren't at all persistent.

I like where you are going there. We have some biblical names on the show.

Aaron
Ben
Jacob
James
John
Michael

Are there any I am missing?

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"Malinois... It's kinda like a bullet. Only it has four legs, teeth, goes around corners, jumps over obsticles, and never misses."

- The DogFather

Tom (Thomas)
Danny (Daniel)
Steve (Stephen)
Naomi
Mary (Sawyer's mom)
Adam (Shannon's dad)
Sarah (Jack's ex wife)
Rachel (lost exp)
Interesting is that Linus is a bible name! Benjamin Linus. And Locke and Ben both have mothers named Emily. Wierd


these are similar-
Diane (Kate's mom) Diana (biblical name)
Alexandra (Alex) Alexander (biblical name)
and then there are various other minor characters that have no significance like matthews, davids, toms, more james and johns. if you look anywhere in life you will find tons of bible names though, my hubby and both kids have bible names and my brother.