Continuity mistake: In the extended version, in the scene where Martha is preparing breakfast, in the interior shot, she places a box of Cheerios on the table. Then she looks out the window at Clark. The shot changes to an exterior shot of her looking out the window, but the angle of the box of Cheerios has changed. (00:38:35)
Continuity mistake: When Clark first meets Lois and the staff of the Daily Planet, he is wearing a handkerchief in his suit pocket. After using it to wipe up the spill from the soda, he stuffs it loosely back into the pocket when he exits Mr. White's office. A couple of shots later, it is neatly folded back into a triangle. (00:53:15 - 00:54:15)
Continuity mistake: During the Golden Gate Bridge crash sequence, a reversed shot of a life-sized 1972 Trans-Am braking hard is shown. The next shot shows a model car smashing into a model school bus, and the car is suddenly a 1965 Corvette. The fimakers have painted it red & white so it resembles the Trans Am. (Timecode is for Director's Cut) (02:09:10)
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.
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.
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.
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 and lays 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.