As mrsMxyztplk mentioned, Superman killed Zod in the 80s-90s comics, but he then self-exiled himself for months out of guilt and a feeling that he was a danger to the world. This synopsis covers it fairly well:
http://sequencedestroyer.tumblr.com/post/41958300720/021-superman-exile In the movie, he was clearly anguished at the time, but we don't see any ongoing remorse (about Zod or any of the presumable thousands of Metropolis bystanders). Maybe it took place between scenes, but it would have improved the movie to show some of it. They certainly could have have traded out some of the miscellaneous property destruction scenes.
Now that I think about it, such a transition could have also covered his decision to operate openly. Yes, he had decided to expose himself to appease Zod, but that's different from being an everyday superhero, throwing the fact of alien existence into everyone's faces on a regular basis.
Like others, Jonathan's character bothered me, but I think it's important to recognize that his motivation for secrecy was not Clark's personal safety -- I think we're projecting that from L&C. Instead, this Jonathan believed he was protecting the world from information it was not ready to handle. Letting a few die for the greater good is an understandable position, though not something we generally associate with Superman.
