When Jimmy and Mr. Whitlock are leaving Dr. Anderson's office the door opens on their right, hinges are on their left. In the hallway when the door closes, it is now reversed.
During the phone conversation at about eight minutes, when the two men who are competing for the Egyptian box are talking, the clock in the background initially says 12:20; but a few seconds later after they cut away then cut back, the clock now says 4:40--a difference of four hours and twenty minutes.
When Superman raises the corner of the pyramid to retrieve the special plant, you can see the stones pivot from the back of the first stone, proving Superman is only raising one stone, not the entire pyramid.
At about 24 minutes, when Kent walks into Perry White's office, he says he's just visited Dr. Wilson. But the doctor's name is Anderson (it's on the doctor's office door).
When Superman is heading off to Egypt, the 'S' on his chest is reversed, meaning that the footage must have been mirrored.
Dr. Barnak fires three rounds from his gun into the mummy case thinking Jimmy Olson is inside. When Superman comes out instead of Jimmy Dr. Barnak fires three more rounds into Superman. Afterwords Superman hands the gun to Jimmy instructing him to deliver Dr. Barnak to the police. He, however, is handing Jimmy an empty gun as all six rounds have been fired.
Sign on Dr. Wilson's office door says "Dr. Anderson".
At about 25 minutes, when they show a close-up of Superman while he's flying, two wires can clearly be seen holding him up.
At about 24 minutes, when Kent walks into Perry White's office, he says he's just visited the doctor, who now has the antidote that Superman flew to Egypt to procure. But Kent didn't see the doctor; it was Superman who saw the doctor. If anyone ever checked up on his story, they'd realize that Kent is Superman.