Richard Donner, the director of Superman, was originally hired to make Superman II. He had made over half of the movie before being fired. Richard Lester was hired to complete the film. So, Superman II contains footage from both the Richard Donner version and the Richard Lester version. See more...
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When Zod says to Ursa to "blow them a kiss my dear" to the helicopter that's firing on them watch as the helicopter is indeed a real military helicopter, then when it loses control it's an obvious model and just before it crashes into the house it's a full size helicopter again but is completely different from the first one that was originally shown.
There are two times in the New York battle when you can see the actors are being filmed in front of a screen: 1. when Superman kicks Non, Superman in on film and Non is hovering in front of the screen. 2. When Ursa is flying towards Non and Superman with the flagpole, she is hovering in front of the screen.
In the first confrontation between Superman and the Zod Squad, Superman gets chased out over the water. In the first two shots in this chase, if you look at the bottom right-hand corner of the screen (at least in the letterboxed version) you can see the wake of the boat that they used to make these two pull-back shots.
When Non tries to fly at the end of the film, but falls into the bottom of the Fortress of Solitude, watch closely. He appears to hit some sort of safety pad after he falls, making the fog around him disperse very briefly, which shows him safely land on the pad. The fog quickly comes back and covers him as he ducks his head down.