Oh, where do I begin with this? First off, as fantastic as that opening on Krypton was, it's nothing but a prologue that literally goes on for 20 minutes and could've easily been cut out of the film without losing a thing--especially since hologram Jor-El explains to Clark virtually everything we just saw in those scenes. What the film should've done is show a condensed version of those Krypton scenes during the moment Clark encounters Jor-El in the ship. That way the film opens with the spaceship crash landing on the Kent farm and then jump cutting to 33 years later showing Clark on the fishing boat. After all, that's when the story really begins.
And while I like Henry Cavill's performance as Clark, I think it would've made more sense for his character to actually go up to the house and ask if he could borrow some clothes as opposed to stealing them (which actually would've been pretty amusing) and didn't mangle the trucker's rig. Also, I would've preferred if Clark's childhood flashbacks were presented in chronological order, save for the last one towards the end of the film. Also, I would've liked to have seen Clark do something heroic like he did on the oil rig after he put on the suit and flew around. Or have a montage of reports of a mysterious flying figure doing all sorts of heroic deeds yet no one knowing who or what he is while we see Superman flying around for the first time.
Also, didn't anyone else think it weird that Kryptonian technology apparently never advanced in the 20,000 or so years that scout ship was buried in the ice?
Another big problem was, as good as Kevin Costner was, the characterization of Jonathan Kent was terrible and, IMO, qualifies him as a nominee for "Worst Father of the Year." This pretty much sums up who he is: "You're not just anyone, Clark. One day, you're going to have to make a choice. You have to decide what kind of man you want to grow up to be. Whoever that man is, good character or bad, it's going to change the world. But you still have keep this side of yourself a secret because people fear what they don't understand, and the world is not ready for someone like you. So you must keep your powers hidden at all costs, even it means letting innocent people die. Because preserving your anonymity is more important than saving lives, including my own. Now if you excuse me, I got to go save the family dog out the car, even though I totally could've avoided getting getting myself and your mom in this predicament as well as forcing you into this moral dilemma simply by turning the car around and not stopping in the first place." *Waves good-bye to Clark as the giant tornado engulfs him and carries him off to the magical land of Oz.*
I'm sure much has been made about Superman's seeming disinterest in the amount of collateral damage and potentially thousands of people who died during the fight scenes--even though they were breathtaking and spectacular. With regards to Smallville, a fat lot of good it did Supes, telling everybody to get off the street and hide in the buildings since those very same buildings end up getting destroyed and blown up moments later. Plus, wouldn't Superman be utterly devastated to see what had happened to the town he grew up in? Plus, his priority is to not go after the World Machine in Metropolis were lives are directly being lost but the one in the Indian Ocean? Or how about during the fight with Zod they actually end up in Earth's orbit yet come right back down to Metropolis again--just to set up the whole "Superman kills Zod" scene of which, the less said, the better.
Also, way too many Macguffins. I mean, by the time we get to the climax, we got the Codex, Kal-El's space ship, the 20,000 year old Kyrptonian scout ship AND the World Builder all in play. Not to mention, I thought the World Builder was necessary and didn't make much sense considering how Zod and his followers, like Clark, are sacrificing godlike powers which could've ensured their survival in order to make Earth more like Krypton, although I guess it was a faster way to get rid of the humans and make for a big action set-piece.
Those are the one's that I can think of right off hand at the moment.