If I were running Facebook, I don't think I'd want to be considered as competing with Mixi, Gree, and Mobage. A lot of people use Mixi almost as a blind dating service, and that's not really what Facebook does.

I'm not much a fan of Facebook, but I could see them picking up there if they really push the photo sharing and contact list aspects of the service, though. For a lot of my Japanese friends on Facebook, I could probably tell you every meal they've eaten outside their house since they've joined. Partnerships with Purikura wouldn't be an altogether bad idea, either.

The first thing anyone does when they meet in Japan is transfer contact info over infra-red. It'd make a lot of sense to integrate it with "friending" on Facebook, since as it is, changing your address means e-mailing your entire contact list, and losing your phone means losing contact with anyone who doesn't e-mail you regularly. There's definitely room for them there - they'll find it if they're actually committed to learning how things work there.