[HaroldMY]

Other than organic traffic what other sources of traffic does Adsense allow?

More importantly what types of traffic don't they allow?

[QysnZWB4]

One thing I'm sure of ; they don't allow traffic coming from adf.ly and similar sources .. some people got banned because of that

[Abofedrorobox]

Would advertisers and adsense care if my only traffic was through facebook?

[HarryMet]

Adsense support all type traffic except traffic from adf.ly, PTC and traffic exchange sites.

[budumol]

It depends I guess on how you get your traffic from facebook. If it's all "legit" meaning you'd be confortable explaining to one of your competitor how you did it because he's unlikely to reproduce it overnight or report you to google, then it's fine.
For instance if all your traffic comes from your facebook fan page, then fine I think.

If it comes from facebook ads I'm not sure, I don't know.

But if it's something else like paying someone who has a trick, then no of course.

[zilsolley3]

Paid traffic and traffic from traffic exchange sites is strictly not allowed. And few other ways as mentioned above are not allowed.

Other than that everything is fine.

As far as facebook traffic is concerned, you need not worry too much unless you are generating exceptionally high amount of revenue from adsense, that's what I feel.