I've gotten the impression from reading up on JET over the past few months that besides the basic bachelor degree it mainly comes down to personality. Which makes sense I guess - even if you have a ton of teaching experience and Japanese language skills, if you're going to run home at the first difficulty then you're a waste of their money. Based on the perks of being a JET it looks like they invest a fair amount of money in every person they ship over, so it's understandable that they'd try to go for someone who will be a worthy investment and stick around for the whole year, if not more.
When I first started looking at applying (for next year) I was thinking of doing extra things to get more teaching/international experience... but now I think I have the basics down and will focus my energies on appearing flexible and open to change during the application process