Why doesn't Miles have his ability to speak with the dead in the alternate timeline? I am presuming his ability is like the Six Sense kids' and it is just some innate gift some people in the world have, but not having it in the other timeline seems to indicate it is connected with Jacob or the island.
We don't know for 100% that he doesn't have that ability in the other timeline. He might have it and in the alternate timeline use it to take to the dead people in the crimes he investigates. Since we haven't had a flashsideways ep. devoted to him (and I'm sure we won't) then we don't know for sure that he can't talk to the dead. I might just be something he doesn't tell all his cop friends and partners about because they would think he was crazy.
But it does stand to reason that if Hurley is exhibiting no paranormal ability in the alt-reality, then it may also be the case for Miles. I do feel they're abilities are somehow connected to the peculiar course their lives have taken in the prime reality. I'm not really sure how though, or if it's anything at all
But Hurley only developed his ability to talk to dead people
after being on the Island. He never was shown to have it before. In fact it might not even be an "ability" of Hurley's. Maybe the "ghosts" just choose him for some reason. Maybe the "ghosts" could appear to anyone if they wanted (Christian certainly does) and everyone has heard the whispers but the choose to talk to Hurley. Maybe because he will listen?
Miles was shown as having the ability since being a little kid (and also after being on the Island) so he could still have his powers, even if Hurley doesn't (since alt-Hurley was never on the Island). I'd assume that Alt-Miles was still on the Island as a child, young Alt-Ben was there after all, so there is no known reason why young Alt-Miles couldn't have been there as well.
But, as a interesting side note, did everyone notice that Mile's dad had both arms when he introduced Hurley?
That means The Incident might never happened in the Alt-reality. If the bomb was the dividing point in the timeline, it went off after the good doctor's arm was already crushed by the machinery at the Swan site. That means he still should have had a fake arm in the Alt-timeline future when he introduced Hurley because the timeline wouldn't have changed until after his arm was crushed.
So that means that the bomb most likely didn't sink the Island (which is good, because I never thought that it did). Also, if the bomb did go off in the Alt-timeline, then the Dr. should have been killed since he was so close to the blast when it happened.
So I think we can now rule out that the bomb went off in both timelines. In fact, it might not have gone off in either timeline.
What? Then what was the flash of light when Juliette hit the bomb? I'm not sure.
But if it didn't go off in the normal timeline (since the Swan was built, Desmond pushed the button, etc...) and it didn't go off in the alt-timeline (the Dr. is alive and has both arms) then did it go off at all?