Zaphod, I've also had trouble seeing Turtledove' Gunpowder Empire or world taken over by the German First Reich as likely. You could have any NEWISH gunpowder empire you chose, but not Rome. Similarly, having the First Reich win France and alot of the rest of the land parts of Western Europe is reasonable to me. But I'm not believing in it being as far ahead of the US and UK in nuclear development as in the book. They're IMHO fun reads, though.
Julius, you're right, of course. Note that classical Greece and Rome had written constitutions in the modern sense, incidentally. But, on paper, the Roman Empire had a Senate, which regularly met. It's just that, well, when Senators that cross their Emperors have a way of suffering or dying, it sure looks like just a piece of paper, doesn't it?
Classical Greece and Italy were pretty advanced on government; they even invented our form of government, republican representative democracy. Check out the Achaean League, which got there by copying the buggy Delian League invented by Athens.