I figure in the sequel that is bound to come, Superman will become more brooding because he killed Zod. Then somewhere in the movie he will become less brooding and upset when he says, "No more killing." From there I don't know what Warner Brothers would do, but I can almost guarantee that will happen.
As you may be able to guess, serious spoilers ahead.
I had a lot of problems with Man of Steel honestly, but in terms of killing Zod, my biggest problem was Superman's lack of... well, heroism. I never got the impression that Superman really cared about ANYONE other than Lois and his family. We never see him really bother to try and help anyone except in for one flashback and that incident with Zod. And then Superman SUDDENLY has a dilemma about killing which had no build-up whatsoever.
At no point does Superman really sacrifice to help anyone. I know being indestructible means it's harder for him to do so, but he could have at least TRIED to stop Zod. I was honestly expecting him to put his hand over Zod's eyes, similar to this scene.
Instead we have the sudden neck snap and Zod's dead. No build up beyond the 2 minutes the scene lasts. It's just sort of sad in my opinion.