Continuity mistake: When Superman brings the flag to the White House, the wide shot shows the wind stopping, and the flag coming to a smooth stop. Immediately after, in the close-up, the flag is moving wildly.
Audio problem: When the three villains fly after Superman, they all gather in a circle and one of them says "Wait there". It can't be Ursa because it is too deep and neither Zod's or Non's lips are moving so it is not them. So, who is it?
Continuity mistake: When Clark is lying beaten up on the diner floor, a man in a brown suit next to him disappears.
Continuity mistake: Before the villains arrive at the Daily Planet, Lois' hair is fluffy and her fringe has a straight cut. When the scene ends, her hair is shorter, and her fringe has some stylish cuts. Also, Jimmy's hair alternates between very short and long, due to Richard Lester's reshoots.
Revealing mistake: When Ursa kicks the astronaut into space, she takes a step back and looks upwards. When this happens you can tell that the film is being shown at double speed. Also, when Clark spins the guy on the chair at the end of the film, he snaps back upright far too quickly.
Continuity mistake: When Zod throws the shotgun after discharging it, it lands in front of the police car's back tyre. But when the dumb one goes to pick the gun up, it is now towards the back of the car.
Other mistake: When Lois and Clark leave the Fortress, the car is driving in the wrong lane. This is due to the fact that the shot belongs to a reused scene from the first movie, where an empty car was remotely driven by Lex, who changed lanes all the time.
Factual error: When the Krypton criminals are on the moon, they speak both to each other and the astronauts, something that's impossible to do in space where there's no sound.
Factual error: When the police car's light is thrown at the boy and it blows up, it shouldn't have happened. The most that would've happened was that the kid would've been knocked off his bike when hit with the light. There is no explosive device in the light, so it shouldn't have exploded in the least like it did.
Plot hole: Lois Lane and other people see Clark Kent unhurt when a taxi hits him and suffers damage, but don't draw the obvious conclusion that there's something extraordinary about him.
Suggested correction: I always took this as an intentional jab at how the people of Metropolis, and Lois in particular, were so oblivious to the fact that Clark was obviously Superman. Still a plot hole, just an intentional one.
Suggested correction: Maybe the cab-driver thinks that Clark is extraordinary, but he is shocked in the first moment, worrying about his damaged car. Later than he realises that this guy is maybe Superman, but cannot find him anymore. Just a guy of millions walking around the big apple.
Other mistake: In the long shot of the Niagara Falls scene, the kid's right arm is way too long.
Revealing mistake: The 3 villains break through the Daily Planet window and fly around the city. Before Zod stops by a beam, Non becomes transparent.
Continuity mistake: When Zod is considering things on the moon, look at the shot of the Earth and the Sun behind him. First, there's apparently a lunar eclipse going on. You see the Earth on the Sun's right side. Then the camera pans over, and the Earth moves over to the Sun's left.
Continuity mistake: Before the East Houston scene, the rear view mirror in the cops' car is skewed in the outside shots, but straight in the ones inside.
Continuity mistake: Man in a yellow shirt disappears after Ursa stops the bus in Metropolis.
Continuity mistake: When Ursa says "your general wishes to speak" her right arm changes the way it's open.
Continuity mistake: After saving Lois in the river, Clark falls on the water and Lois cries "Here.", a split second later she has changed position, being now turned around and she has also moved 3 feet into water close to Clark.
Continuity mistake: When villains fly through Perry's window the reflection of the lights disappear and the blinds flutter without any problem, revealing that the glass was taken out to allow for a safe jump.
Continuity mistake: In the bar in East Houston, the man that challenges Ursa to arm-wrestle has his right arm and elbow on the table. In the next shot they're down.
Continuity mistake: When Ursa sits down to arm-wrestle, a man with a red jacket who was sitting several feet to the left, suddenly appears on the back close to the guy with a Coors T-shirt.