If Facebook starts spending their $16bn of cash in companies with "rich" valuations which provide equal or lower implied FB growth rates (market valuation wise), FB's stock is going to plummet. Having a pile of cash can be a problem.
Any country with CCTV or public surveillance (perhaps satellite?) could use FB's pics and Face together to track who's where and when. It'd be a synergy for surveillance, I just wonder who's got the best technology to do it.
That's not how the Face API works. An app needs the user to be logged into FB, and then the app can attempt face recognition for that user and their direct FB friends only. For a government to do this it would need collusion with Facebook; with or without the Face API.
As for satellite surveillance - even if modern military satellite imagery had that kind of resolution (it doesn't), and ignoring atmospheric conditions (a bit hard to do for the UK), it's hard to imagine how they would do face recognition from the tops of peoples heads.
Makes more sense for Google to buy them. They could do two things with them:
1: build the technology into their Google Glasses so peoples names pop up as they come into view
2: redirect face.com to Google.com.
That second option would be well worth the 100 million too. Consider this: after you visited face.com once every next time you want to go to facebook.com and type in 'face' your browser will auto-complete to face.com
Doesn't Face.com have an API? I think the active users of that would be upset if all the documentation/etc. for it just disappeared and started redirecting to Google.
More to the point, a free API. I can't see Facebook or Google keeping the API around if they acquired Face.com, which would be very sad. Of course, it would be a technology rather than a user acquisition, so I don't suppose whoever was buying would care that much.