What is the significance of Koizumi noticing Kyon's mole? What is the significance of Koizumi noticing Kyon's mole at the end of Lone Island Syndrome? 

I don't think there was this ever an explanation made in the anime... was there any context given in the light novel?

http://www.youtube.com/watch?v=gYHm7N3EtmQ#t=44s
I don't have any hard evidence to back it up, but I always assumed that it was at that point that Koizumi actually started taking Kyon seriously.  Instead of just looking at what he seems to be at first glance, he started peering into him at greater depth.  And, since it's mostly a comedy series, that greater depth involves a mole.