As a follower of the comics for a long time, this is consistant with the story.
After the crisis of infinite earths, Zod shows up with his henchemen from another dimension. In this dimension, Zod killed superboy and went on to conquer his home there.
They get loose on earth and superman uses green kryptonite to weaken them. As they are weakened, Zod starts ranting how he will get strength back soon and then try to wipe out humanity on earth.
Realizing that Zod could not be controlled and couldn't be easily stopped, Superman turns the Krypontite on all three killing them.
This sends him into a deep depression and he leaves Earth, no longer feeling worthy of being it's protector. It is during this time that come to terms that while the action was necessary, he would never kill again, setting the framework for the Superman for decades after that.
In all, not bad, I think they accurately portray how the military and government would react to discovering someone as powerful as Superman. I thought the attempt at trying to track his movements to learn his weaknesses was accurate. Also the whole "Look I have glasses, nobody can recognize me as superman" was a weak element to the story, a hangover from the silver age. Having those that know Superman recognize Clark Kent makes more sense.