Factual error: When Clark speaks to Jor-El for the first time in the Fortress, Jor-El says "I will have been dead for many thousands of your years..." Fine in theory - Baby Kal-El travelled to Earth at above light speed so time passed differently for him. However, as such, wouldn't Jor-El have seen Earth as it was thousands of years ago? Which also makes there a problem with all the things Kal-El was taught during his voyage to Earth, as Jor-El references Einstein by name, for instance, and he would not have existed at the point when Jor-El sent him to Earth.
Revealing mistake: In several scenes Superman has fillings in his teeth.
Plot hole: After Superman has reversed time the Hoover Dam reverts to its previous undamaged state as it should, but Jimmy Olsen should then have been replaced back on the dam. Instead he interrupts the potential kiss between Lois and Superman and complains of being abandoned by Superman in the desert.
Suggested correction: Superman is moving at speeds fast enough to turn back time. He can spend 5 seconds to yank Jimmy away from the top of a dam he knows is going to be destroyed just to be safe in case he can't actually stop it all from happening again.
Factual error: When Superman is turning back time by flying around the Earth, right before he starts orbiting the Earth is spinning way faster than it actually should be. If the Earth actually spun that fast, a day would pass by every 1.44 minutes.
Plot hole: Superman could have easily caught both missiles, proven by how fast we see him flying around the globe just a few minutes later. He's fast enough to circle the globe multiple times in seconds, but struggles for minutes to catch the missile.
Suggested correction: Superman had never flown that fast before in the movie. It could be argued that he was still in the process of discovering and pushing the limits of his powers and it was the emotional episode of losing Lois that motivated him to push himself.
Revealing mistake: When Jor-El is placing the baby Kal-El into the spacecraft, you can see his Rolex under his sleeve.
Visible crew/equipment: Just after young Clark Kent jumps in front of the train, there is a close up of the train speeding by with a very visible camera in its reflection. (00:30:00)
Continuity mistake: Kal-El's cradle arrives on earth, flies zooming past the Kents' car, which is driving in the opposite direction and crashes 500 meters behind the vehicle. The car keeps moving for about 200 meters and then pulls over. A brief shot shows an intact curb on the right. However, when Jonathan Kent gets out of the car, everything changes: The cradle has moved 700 meters ahead and lies next to the car; and the immaculate field is now destroyed by a huge ditch.
Visible crew/equipment: Near the beginning when Lois and Clark are walking out of the Daily Planet, Clark gets stuck in the revolving doors. But, look closely at the glass door, and you can see Richard Donner (confirmed in Superman expanded commentary) holding the door so that Christopher Reeve can get stuck.
Continuity mistake: When leaving the Daily Planet for the first time together Clark gets stuck in the revolving door behind Lois. He lets her go through ahead of him and gets in the next section as the door revolves. Cut to the exterior of the Planet when they emerge (just before they meet Rex Reed) and Clark is in the same section of the revolving door as Lois.
Audio problem: In the plane, when the Captain says "I'm not too god, what do you think" his lips aren't moving.
Continuity mistake: On the Golden Gate, the blue beetle skids and stops with the rear tyres on top of a painted white line. A frame later the car is on the middle on the white line.
Continuity mistake: When Otis is reading the paper about the meteorite found in Addis Ababa, the amount of chocolate in the candy bar increases or decreases depending on the shot.
Continuity mistake: The lights on the heliport keep swapping from facing the ground to pointing at the sky between shots.
Continuity mistake: The telephone poles close to the gap on the railroad disappear in the wide angles.
Continuity mistake: Inside the cab arriving at the Daily Planet, the fruit stall has no van behind. Immediately afterwards, a van appears.
Revealing mistake: When Lois is at the heliport, watch the wind flag on the left: when the helicopter arrives, the roaring wind from the vanes makes the flag move up and get stiff. In the close-ups, you keep on hearing the sound but the vanes are off screen. Watch and you'll see the wind flag is down, thus revealing that the engine is off and that the sound we are hearing is fake.
Other mistake: When Superman and Lois are flying through the clouds, there are a number of shots in which we see Superman from Lois' point of view. If you look closely, you can see that Christopher Reeve is not being suspended in these shots, but is, in fact, kneeling to look as though he is flying. You can tell by the profile of the red trunks.
Continuity mistake: Liz places her kitty on her right shoulder and on the next shot the cat's gone.
Continuity mistake: In the extended version, when Superman talks with his father in the Fortress of Solitude about being a hero, one shot shows the crystals reaching up to Superman's waist. In the next shot they are at ankle level.
