I know this is an old post but he didn't "pick on" Kazakhstan. It's just a country that people in the West are so ignorant of that it basically allowed to him create his own country. The whole point is that Borat is a simple guy, who is very poor, backwards and extremely bigoted, which makes other people comfortable in revealing their own bigotry to him. It's those people that he's mocking, not Kazakhstan.
He couldn't do it with, say, Saudi or Iran, because their society is a bit more well known in the West. Plus I don't think they'd react quite as diplomatically as Kazakhstan did.