Continuity mistake: When Non rampages the Daily planet, the grey file cabinet lying on the floor changes positions before and after he enters.
Continuity mistake: Superman descends to stop the big truck from exploding and lands in front of it, by the cabin. A frame later he is seen landing a meter before the truck.
Continuity mistake: When the antenna is about to crush the pram, the mother is first behind it. A second later she's by the side. Then a second later she's on top of it, and a second afterwards slightly covering it. Boy she moves FAST.
Continuity mistake: Inside the Fortress of Solitude, when Non jumps to fight Superman, before he flies, Ursa and Lois are looking at Superman. A mere frame later, when Non starts to fly, both girls are in a different position fighting against each other. It's a really awkward and sudden change.
Continuity mistake: At the end, in the Fortress of Solitude, Lois' hairstyle keeps changing from fluffy and dull to smooth and stylish.
Continuity mistake: After the hide and seek game in the ice cave, Luthor's fringe constantly changes length and style.
Continuity mistake: Clark steps out of the diner and the waiter has his hands on his chest. A shot later his hands are on the counter.
Continuity mistake: After being hit by a cab, Lois calls Clark and the people behind her change in a split second.
Continuity mistake: In the big fight scene in Metropolis, after Ursa chokes Superman, Non descends and wires holding him is visible.
Continuity mistake: When Superman is about to stop the elevator, he flies with one arm up the other down. A frame later in a new angle both arms are up.
Continuity mistake: On Krypton, when the guard gets caught, Non's hand is at chest level. In the close-up it is at belly level.
Other mistake: When the three villains jump out of the Daily Planet window they just break some glass; however, from a ground level shot huge chunks of concrete are falling. This is more dramatic, indeed, but senseless.
Revealing mistake: During the Metropolis battle, after Non and Super go down through the pavement, Non is launched upwards thorough the concrete. Check the people around, specially the cop on the right. They are blatant toys (note the cop's weird arms), revealing it is all a miniature set.
Audio problem: When Non is launched towards the Empire State a man says "Wow, home run!", but his lips are not in sync.
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.
Continuity mistake: Inside the White House the cops fire 3 or 4 times at Zod but the wall and statue behind him have at least 15 bullet holes.

Other mistake: When the elevator explodes there's a shot of the Phantom Zone and Ursa is a totally different actress. Different to the other unknown actress used on the first movie, which is also listed as a mistake.
Continuity mistake: Right after Clark reveals himself to Lois in Niagara Falls hotel room, by his hand falling into the fire, he backs up to where the bed and lava lamp like column is behind him. In that shot, there isn't much of the "lava" in the column. The scene cuts to a shot of Lois and then back to Clark and suddenly there is a lot of "lava" in the column. (00:53:05)

Continuity mistake: In the diner, whilst Clark is asking the bad guy to step outside, the waiter is leaning over the baddie's right shoulder. When the angle changes he is leaning on the left shoulder.
Continuity mistake: When the villains are being judged, for a brief second they change positions, Zod being on the far right instead the far left.