I read a fic a while back where Clark came back from New Krypton missing a hand. Dr. Klein made him a robotic hand with a matching glove for his remaining hand so that it looked like he was wearing gauntlets. That way it looked like it was just a new fashion statement from NK. I'm not sure what all the implications are for using a robotic hand with his powers, though. How strong is the hand, and how well is it attached to his arm? How much could he lift before the robotic hand just fell off? How well could he control it - if the hand has fingers and whatnot, how much dexterity would he have?
I like Lara's idea of Superman levitating to hide an injury to his lower leg or foot, but it would be hard to hide if he was missing any of his leg above his boot. If Superman has a prosthetic that he's trying to hide, what happens if it melts or catches fire or breaks? If Superman is publicly maimed and Clark is hiding a prosthetic, what would happen if he's discovered? I could see Clark and Lois hanging out watching a movie or something, and she wonders why he won't take off his shoes and relax and ends up discovering his fake leg.
I think that if Superman could figure out how to hide his injury, it would go a long way to help people not realize that he's Clark. Either way, though, he's likely to be found out.
What about a more subtle injury, not necessarily losing a foot, but something that leaves him with a permanent limp? One persona could hide the limp, but what happens when he's exhausted or not paying attention and limps at the wrong time? Or doesn't limp when he's supposed to?
Another related problem Clark could face is a visible scar. It could be more subtle, like along the hairline or on his hand, or it could be a blatant red mark across his cheek. Would he try to cover it up with makeup, or would he stage an incident in the other persona to just happen to very publicly get injured in the exact same way? Maybe Metallo gets Superman across the face, and it doesn't heal right because of the kryptonite. Then later Clark stages some accident in a public place that gives him an apparent gash across his face, too. Of course that just raises the question of what he would do if the scar did eventually go away. Claim that Superman healed, and Clark got plastic surgery? That's a bit much in the way of "coincidences".
I should stop reading these challenge posts. They give me too many half-formed ideas that I'd love to read if someone wrote it, but I don't have the energy to write myself. I've got too many stories in my head and in progress already that are currently going nowhere; I shouldn't add to my list. :p But it's just too entertaining to read everyone's ideas!
Maybe the new limb doesn't have any superpowers. Maybe it makes him go all Jekyll and Hyde and splits his personality... again. 