Visible crew/equipment: When Superman and the super villain are fighting on the moon, when Superman flies in and lands at the beginning of the fight, you can see the cables that are suspending him.
Plot hole: Superman traps the supervillain (whose power depends on sunlight) inside of an elevator to incapacitate him. Superman then ripped the elevator out of the building. He then plants it on the far side of the moon. Later on, sunlight starts to shine into the elevator through a slit at where the doors meet. The villain of course recharges and comes after Superman again. Now, if light could get through that crack there, then why couldn't it get through when the elevator was ripped out of the building in BROAD DAYLIGHT?
Factual error: When the villain takes the reporter into space (the earth is just a circle off in the distance), then weakens and lets go of her, not only does she start to fall, she starts to fall straight down and has to hang onto him. (Oddly enough, HE's NOT falling). Did somebody inject normal earth gravity into mid-space?
Plot hole: When Nuclear Man sees a picture of Lacy Warfield on the newspaper he decides to go after her. When confronted by Superman he asks "Where is the woman?" Superman responds that he'll never find her. How could Superman know which woman Nuclear Man was talking about? There was no indication that Superman knew that Nuclear Man was looking for Lacy.
Continuity mistake: When Nuclear Man arrives on Earth, he enters a shady place which makes him loose his power and cools his body, producing some frozen-like smoke. The next two times that he enters a dark place (inside the elevator and in space) he doesn't produce the smoke. FX budget problems here?