I have two theories that may fit with this, but they don't go together:
1) What if the two islands or two ends of the main island have different properties, sort of like the poles of a magnet? What if the main island where the hatch and losties are has healing abilities, and what if another part of the island or the other island cause people to age quickly?
2) (I like this one better) What if the only real mysterious property of the island is that it speeds up time and/or the aging process? This would explain Locke's healing so quickly - it would have healed anyway, just slower. I've been assuming that is because of the healing properties of the island, but perhaps not. It doesn't explain Rose's cancer going away, but maybe it hasn't or maybe she was actually getting better already and it was sped up by the island. To take this a step further, maybe there is a place that the Hanso Foundation is involved with also where time/aging is slowed down. I remember in TLE there was something about Alvar Hanso being much older than he looks. I'm really liking this theory, the more I think about it... perhaps the time speed up/slow down thing is the property that allows them to do all kinds of other experiments. More to come.