I think that the prequels develop it's own world and do an excellent job of standing on their own. Only those who have seen the OT would actually be trying to connect the dots. Hell, other than R2/3PO, the Emperor & Vader, Obi Wan and Yoda, nothing carries over. It's a completely different time and world, and films because of it.
I'll give you III, but why would you only see it? Going in, it's job wasn't to be a stand-alone, but to wrap up the things seen in the previous 2. Even witrh the Emperor, they didn't revela until Ep III. You never saw his face, just always a shadowy cloaked figure, and he wasn't known to be the same until the final reveal. Of course, if you saw the OT, you knew that Ian McDiarmid was playing his original character.
Ep III wraps up the war, and once it's over, Papaltine can't allow everything to go back at it was before; he'd be starting over. So he positions ervything to be over all at once.