What absolutely killed it for me wasn't the destruction of Metropolis or the over the top fight that surrounded it, it was the complete absence of any kind of proper organisation on a national level either in its wake or in the hours leading up to it. This wouldn't bother me if they hadn't spent so much time inserting military characters into the plot.
The military finds the ship, which Clark hears about through a series of very fortuitous meetings and then they're also perfectly happy to let Lois Lane to get in that action also.
The military finds <url=http://en.memory-alpha.org/wiki/Nero>Nero's Zod's ship and just sort of sits on it for bit.
The military captures our hero, regardless of any willingness, and proceeds basically be the driving force behind the plot up until the point where Jor'El decides to tell an unversed layman how to destroy Zod's ship (which is actually another annoying point in that the instructions boiled down to "Hit Object A with Object B" and is surely something he could have explained to Kal'El) because he wants to set his son up with a hot piece of ass.
Then there is the complete lack of agency in any of the female characters, besides German Michelle Rodriguez (another great actress pigeon-holed into tough chick for the rest of her career, congrats Nolan/Snyder) who had a good showing in Pandorum and probably could have done much more... but I digress. Clark/Kal/Superman saves Lois Lane three times in one film, THREE TIMES and then is perfectly in the mood to give her a nice long kiss immediately after watching countless thousands of people die as a densely urban area is levelled by an alien gravity weapon. Good show. And Lara, who basically existed within the context of the plot to push a button (regardless of all the stuff leading up to that button, I'm discussing the actual influence of the character directly on the plot) and then accept death after she watches the love of her life and the father of her child get murdered infront of her... and doesn't particularly try to claw Zod's eyes out?
I've gone on a massive tangent here and I could go on for a while but to get back to my point, the entire US military and emergency/disaster management apparatus appeared to just sit back in the third act with the attitude "Meh, let the air force handle it."
Why, after an alien attack on the heartland of America, wasn't a state of emergency declared?
Flights grounded? Some helicopters were just hanging around between buildings in Metropolis.
National guard and reserves mobilised? I didn't see any.
First responders at full readiness? There was one scene with a cop trying to do some crowd control, but all I really needed was a 5 second panning shot of some EMT's getting injured into ambulances, some firemen dealing with the Burly Brawl induced destruction or even some police officers working to evacuate civilians from the epicentre of the destruction.
Evacuation plans for major urban centres prepared? See above.
Literally crippled my suspension of disbelief, then the third time he saves Lois finished it off with a headshot. It wasn't a bad film, it was just sufficient.
EDIT: Plot goal for Zod was to ensure the continuation of his species as he desired. He had enough of the codex to activate the Genesis Chamber in that outpost but then decided "I better take this extremely valuable ship, which is basically the entire goal of my invasion of this backwater rock, and use it to attack some dudes."