I would NOT have Superman being the reason Zod's on earth.
That tornado scene needs to go, along with Clark's nonsensical out of character decision to not help his dad, even through normal nonpower means. Or at least not make it look so easy for Clark to have walked like 10 feet to his dad and helped him back to the overpass. At the very least, they should have made it impossible for Clark to reach his dad in time without his powers. Forget it, Clark not saving his dad with or without his powers just pisses me off so yeah that whole concept needs to go.
Superman tackling Zod recklessly right into town, leaving Martha behind with a bunch of kryptonians who very easily could have killed her if they'd thought of it.
I agree on saving the kiss for the next movie, and replacing that with Superman and Lois looking around in horror at the destruction. And have Superman using his xray vision or superhearing to look for survivors. And show him help rebuild Metropolis.
Show the city being evacuated when Zod's ship appears above it and before the world engine ray starts destroying it. Not everyone would leave, so people would be in danger, but the implied body count would be a lot less.
Show Superman actually being hurt or close to defeat. Show him using his brains to come back from defeat. Show him using his brains for anything.