So how do they make sure it's not domestic?
http://www.npr.org/2011/11/04/142029141/cia-analysts-comb-so... I'm gonna go ahead and guess the domestic part exists, but is just more top secret. As if they would limit themselves to foreign IP addresses. Gimme a break. This probably isn't even technically spying, since all this stuff is public. I've read in the past that the CIA's biggest intelligence source is newspapers from around the world. Go figure.
And yeah, I am sure that they don't keep it to overseas stuff. I'm sure that's just PR. Like you say, since these are public posts, I don't see why they couldn't sort through them anyway. I wonder how long you need to tweet crazy stuff before someone takes notice. I suppose it's a matter of how crazy.
I suppose there are probably algorithms that search for tweet words and patterns. I would think there are too much data to just keep an eye one.