Some of Gene Hackman's scenes were actually filmed with a body double. That's because Gene Hackman quit before all of his scenes were shot. See more...
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Visible crew/equipment: Ursa throws the sewer lid at Superman sending him flying backwards into the car windshield. Watch the sewer lid carefully when Superman actually hits the windshield. You can see that the sewer lid was actually attached to a belt around his waist so that it would stay in place for the shots where he is flying backward through the air.
Factual error: After Superman accidentally frees the phantom zone villains with the exploding hydrogen bomb, they start flying towards the moon. The sleeves in their clothes can be seen fluttering around. This would be impossible because there is no air in outer space, hence nothing to cause resistance against the clothes.
Other: When Clark and Lois are on their way to the diner, the wide shot of their car driving along looked very familiar. In fact, it was footage used in the first movie, where the car was used as part of Lex Luthor's "real-estate" plan and was run on remote control. If you look closely in part II, no one is driving the car yet you hear Clark say to Lois, "Hey, you seem pretty quiet over there...."
Plot hole: Before the trio crashed into the Daily Planet (just before the battle with Supes), they were heard flying outside the building. For 3 superbeings with the ability to fly unaided, they sure sound heckuva lot like jet-propelled aircrafts. Jet aircrafts are noisy because of their engines, but superpeople?