Continuity mistake: After crushing Zod's hand, Superman sends him flying away. Luthor's head turns around twice.
Revealing mistake: When Non falls on Superman and breaks the concrete, the hole opens before Non falls on him.
Continuity mistake: When the ring falls on the villains, Non is looking down and a split second later he is looking up.
Revealing mistake: In the ice cave, when Superman makes himself invisible, watch Zod's head jumping slightly to the back, revealing where the scene was edited to achieve the effect.
Continuity mistake: When Non is about to break Perry's desk in half, Jimmy and Lois are standing very close to each other. A split second later they're farther apart.
Continuity mistake: When Lois prepares orange juice, Clark lowers his left arm and sneaks it behind his back. A second later the arm is up.
Continuity mistake: Zod makes a short jump from the white car to the Marlboro truck, but in the next shot we see the two cars are several feet further apart.
Continuity mistake: In East Houston, the army jeep is passing by a brown car, then Ursa talks and we hear the jeep engine coming close, but when the image focuses back on the jeep it is several feet behind the brown car, instead of being in front of it.
Visible crew/equipment: Wires holding Superman are visible when he is about to stop the elevator.
Continuity mistake: In East Houston, while the helicopter fires at the 3 villains, a soldier runs behind Ursa and she is left totally alone. In the next shot he is behind her, running away again.
Continuity mistake: When Clark crosses the street before being hit by a cab there's barely no people behind, in the next shot there's a lot more.
Continuity mistake: When Clark comes out of the river one shot shows the back of his jacket with one half up and another down. When the angle changes the entire jacket is up.
Revealing mistake: When the Empire State antenna falls down the wires holding it are visible.
Audio problem: Most of the times when the French terrorists talk, their lips are not in synch or their mouths don't move.
Continuity mistake: When Ursa throws the sewer lid to Superman, first she is standing in the middle of the street but in the next shot she is close to the curb, by a yellow cab.
Revealing mistake: In the New York battle scene, after Ursa distracts Superman, Non punches him and he goes flying backward into a building. Watch very carefully along the bottom of the screen. You can tell that Superman isn't even matted in from the chest down. Where is the rest of him?
Revealing mistake: When Non tries to fly at the end of the film, but falls into the bottom of the Fortress of Solitude, watch closely. He appears to hit some sort of safety pad after he falls, making the fog around him disperse very briefly, which shows him safely land on the pad. The fog quickly comes back and covers him as he ducks his head down.
Continuity mistake: When they are in east Houston, Idaho, the helicopter gets knocked out of the air and lands upside down onto a jeep. You see the pilot get smashed into the seat of the jeep real hard and yet seconds later he walks away unharmed.
Revealing mistake: In closeups, you can see Lex Luthor has a bald cap on.
Suggested correction: Much too vague. What scenes are you referring to. And how can you tell, other than knowing that Gene Hackman isn't really bald?
Audio problem: In the Fortress of Solitude, when Superman kneels before Zod, we hear Lois sobbing, but her mouth and body don't move.