There was a couple of lines I wanted to shout out during the movie.
First was when Superman surrenders himself and everyone was training their weapons on him. All I could think of was the line from the Doctor Who episode "A Good Man Goes to War" where he says "Please, point a gun at me if it helps you relax. You're only human. "
Second was in the Zod fight when Zod took hold of Superman's cape and swung him around, all I could think of was the "NO CAPES!" line from The Incredibles.
As for "the Superman we know wouldn't have killed Zod and would have prevented any collateral loss of life during the fight with him", remember he's new at this. Never faced anyone or anything that taxed his abilities and never fought in a crowded area before. This is rookie Superman, new to the whole saving the world thing. And more people would be killed if he lost again Zod so he couldn't give Zod an opening such as stopping that gas tanker from exploding into that parking structure where moments earlier we see people watching the fight. Superman loses, everyone loses. The only thing going through his mind was stopping Zod. Period, end of story. It's the trolley problem just on a much bigger scale.
And Zod wouldn't be willing to move the fight to a safer local because threatening humans lives gave Zod an edge. If he one he would spend the rest of his days gladly killing off each and every human personally just to pass the time.
Sore points
Clark, when the bad guy is suffering sensory overload like you intended him to get, DON'T tell him how you learned to overcome it! Sure Zod might have been able to figure it out on his own but it would have bought you more time.
Jor-El taught Lois that the big secret was turn on the phantom drive on the baby carrage and chuck it at the Zod's ship. Hope she took notes on such a complex and nuanced plan.
Jor-El designed Zod's ship/former prison yet the best he could do once uploaded was to change the atmospherics and open and close doors. Couldn't say jump the ship deep into Jupiter's atmosphere or say into the Sun. Nope just parlor tricks and pranks.
How many times reporters and the Weather Channel have to tell people don't take shelter from a tornado under an overpass before people listen?
And if you see a giant space ship descending over your city, you leave, NOW! Not when it starts the thumper beam and not after you realize the radius of the thumper beam is increasing. And you certainly don't ever run toward the giant space ship! What, nobody remembers ID4? At least one of the Daily Planet trio knew to run laterally from the falling building.
Other Points
According to the tombstone and assuming the movie is set in 2013, Clark was 17 when Jonathan was killed.
Only let the alien kiss you after the third time he saves your life, it's a rule. She's going to have to get into some more peril if she wants him to get to 2nd base.
So we have a Lexcorp building and a Wayne Corp satellite. Well it's something at least.
Edit: Edited for Houtex