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?
Revealing mistake: When Superman saves the people that Nuclear Man throws up into the air, as they lower you can see the support wires holding them up.
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.