He shouldn't need to hire a fact checker. He just needs to realize that his error rate is too high when he just tosses off these historical claims based on his own background knowledge, and stop doing that. If the claim is really central to the argument, then take the time to check it. If it's not that important, then just leave it out.

Unfortunately, public intellectuals in our current society don't hold themselves to these kinds of standards (which would have been considered obvious for public intellectuals a couple of centuries ago), and no one else holds them to it either.