Visible crew/equipment: In the town in Idaho when General Zod and his crew first visit, watch when the boy's father (elevated by Zod's finger) falls to the ground. You can see the pad under the dirt when he hits it.
Revealing mistake: In the final scene, Superman is returning the White House's flag to its rightful place, flying over the fountain on the lawn...which is frozen solid in place. Obviously a photo backdrop.
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.
Revealing mistake: When Zod lifts the boy's father with the beam of white energy, watch closely when he raises him up past the telephone pole...he 'clips' right through it, or rather the pole clips through him, as if he is transparent.
Visible crew/equipment: When Superman is fighting Non under the New York Streets (in the sewers), manhole covers start to jet up in the sky. When the first manhole cover shoots up you can quite clearly see the gas tube in the hole and the gas cylinder attached to the cover.
Other mistake: 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...."
Other mistake: At the end of the film Superman puts the US flag back onto the Whitehouse. Whilst he is speaking to the President through the hole in the roof the flag can clearly be seen flying in the wind, but his cape is completely still.
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.
Continuity mistake: There are two external White House shots in the film. The second is a still shot, and should take place at least a few days after the first. However, it is a frame from the earlier shot, with the same person standing in the same spot on the lawn.
Revealing mistake: In the beginning, when Superman is flying to the Eiffel Tower, the last scene that shows him flying towards the tower, you can see the wire Christopher Reeve was attached to as he swoops down. The wire stretches all the way across as Superman glides down.
Visible crew/equipment: In the shot where Zod walks on the lake's water, there is a platform visible just under the water's surface.
Continuity mistake: In the opening scene where the three villains destroy the energy crystal and the lights go dark and the rings descend upon them, the light that surrounds them is shown coming down from the ceiling. But, when the dome opens, the light surrounding them shines up from the floor. (As also seen in Superman: The Movie.)