One great thing about Persona is that it doesn't have to get involved every time I log into some website. The keys can be cached, so Persona doesn't need to know which websites I visit the most frequently, how long I spend on each site, which pages I read, etc. Persona just provides the identity and stops there. In that sense, Persona's very design makes it an unattractive target of surveillance. Not much data there.
Right now, Mozilla knows my email address, my (hopefully salted and hashed) password, some keys associated with said password, and the set of IP addresses from which I ever accessed Persona. Maybe also the set of IP addresses from which its key was requested, but that's not a particularly useful piece of information when NSA is trying to figure out what I'm up to.
However, Two of the planned changes to Persona gets me worried a little. The first is that Persona will allow people to add multiple email addresses to each account and choose which one to use at any given time. This means that if NSA gains access to the contents of a Persona server, they'll be able to link several (seemingly unrealted) email addresses to the same account. If you're a heavy Redditor, imagine that somebody will be able to find out every throwaway account that you made and abandoned over the years to talk about things you don't want traced back to you. That's the sound of the Eureka! that the NSA agent utters when he finds out that the person who has been posting anti-factory-farming comments all over the place is actually the same guy who retweeted some anti-Esso catchphrase, who is the same guy whose personal blog contains pictures from a recent trip to Pakistan.
My second worry is that Mozilla expects email service providers to serve as a Persona provider for their users. If I'm not sure whether I want to trust the Mozilla Foundation (the good guys) with information about my various alter egos, I'm definitely going to be wary of giving Google, Yahoo, and Microsoft the same kind of information. Although it's possible for you to be your own Persona provider, realistically, not many people are their own OpenID providers at the moment, and not many of them are going to be their own Persona provider, either. Decentralization is often advertised as one of the better features of Persona, but I suspect that it's going to remain little more than an advertisement. Everyone else will just use Google-hosted Persona with their Google-hosted email, with no real improvement of privacy.