Continuity mistake: In the scene where Clark is on the fishing boat and is about to be "crushed" there is a bundle of rope that is dropped on the deck. The bundle changes from what looks like cut up strands when it drops, to a nice looped up solid piece when the camera cuts to him picking it up.
Continuity mistake: When the woman is trapped at the end and Perry is trying to save her, the same car is crushed twice by the force of the world engine.
Factual error: In the final scenes when Superman is fighting the enemies in Metropolis, even though half the city has been destroyed, the lights are still on in many buildings. In reality, the destruction of a few skyscrapers would be enough to trigger the shutdown of the electric substations that serve the city and all the lights would be off (as happened with Hurricane Sandy). (02:00:00)
Continuity mistake: When Superman is fighting Faora and Nam-Ek in Smallville, his head is held to the ground by Faora. In this shot his hair is over his forehead. The camera switches quickly to a shot of the two holding him down and then back to him - his hair is now off his forehead. (01:35:00)
Continuity mistake: In one of the scenes where he is being bullied and is pushed against a fence by a group of kids, he's pulled out of the car while he is holding a book. Later when he is pulled up he uses his right hand, but in the shot afterwards the fence pole is bent by his left hand.
Continuity mistake: When Clark pushes the school bus out of the river the front doors are open, but when he returns with the class bully the front doors are now shut.
Revealing mistake: When Zod is arrested, his bloody facial wound is a glued-on prosthetic.
Visible crew/equipment: As the two helicopters land, and as the soldiers come out, the camera equipment is reflected in the glass.
Revealing mistake: At the end when the drone crashes in front of the car and the soldier gets out you can see the footprints in the sand from previous takes, in the exact spot where he steps.