I tried it out on a site I was building a couple months ago. Every time I had a non-"techie" user try it out, they got confused. What's this popup? What's Persona? What am I signing up for exactly? It was just bad UX.
That said, I think there's a very real need for what they're offering. I don't want to store passwords myself, even if they're hashed. I also don't want to re-implement forgotten usernames, passwords, reset emails, etc. It's a bother, I'd rather focus on my app rather than a solved problem like this, and to be honest I don't quite trust myself enough to get it 100% right.
So, I think it would be the best of both worlds to offer auth as an API rather than providing their own experience. As in, I could just call Persona.login("username", "password", ...) and get back an assertion. I really hope they go in this direction.