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?
Deliberate mistake: The kid who falls into Niagara Falls spends 28 seconds falling before Superman catches him. Niagara Falls is 51 meters in total height. Considering how fast something falls, the kid should have hit the water long before Superman ever entered the scene. (00:39:30 - 00:40:00)
Continuity mistake: When the three super villains attack the astronauts on the moon, as Non lifts the lander's leg, there is a shot of the astronaut inside a collapsing cabin. It is like there is something crushing the roof inwards, but all three super villains are accounted for, with Zod sat in the moon buggy, Ursula standing next to him and Non lifting the lander. This happens twice in the space of a few seconds before Non jumps on top of the lander to crush it. (00:27:25)
Audio problem: In the Fortress of Solitude, when Superman kneels before Zod, we hear Lois sobbing, but her mouth and body don't move.
Deliberate mistake: French officers and firemen speak in English between them.
Continuity mistake: Inside the bar in East Houston, Zod pushes a man backwards, but the next shot shows the man flying as if he had been thrown upwards.
Revealing mistake: When Non goes through the pavement, the hole reveals it's a foam made floor.
Visible crew/equipment: When Non crashes Perry against the ceiling, a crew member's hand is seen holding Perry.
Revealing mistake: During the big fight in Metropolis, the close-up of the pram shows its empty or with blatant bundled pieces of fabric to simulate some sort of baby.
