The good old man of steel. How do we change him? Or perhaps the more important question, should we change him?
I'm inclined to say no. Or perhaps more aptly, we should roll him back a bit. I always liked the idea of superman as the immigrant metaphor far more than him being the uber-American.
The other big change would be tone down how much actual heroing we see on page. Not that I don't like seeing superman being the original superhero, but I think there's a lot more fun to be had with him doing character stuff than there is with him punching Zod in the face (or breaking his neck). I'd probably focus his opening arc on some fun philosophical questions and moral dilemmas tossed his way—we know Superman can do anything, but should he? Have a civil war going on in Quraq, Kasnia, or whatever fictional DC country works best. Supes wants to do something about it, but the more he gets involved the messier the whole situation gets. Avoid any of the usual easy outs like one side being totally evil, or it all being an evil scheme by Luthor or another supervillain. Just a nasty, messy situation he has to find his way out of.
As for the rest of his cast, most of them are okay. Lois Lane plays off him well (and should take back her romantic interest role). I'd maybe put a touch more emphasis on her army brat roots to make her less of the iconic damsel in distress, but that's something the comics have been doing off and on for a while.