Continuity mistake: When the three super villains attack the astronauts on the moon, as Non lifts the lander's leg, there is a shot of the astronaut inside a collapsing cabin. It is like there is something crushing the roof inwards, but all three super villains are accounted for, with Zod sat in the moon buggy, Ursula standing next to him and Non lifting the lander. This happens twice in the space of a few seconds before Non jumps on top of the lander to crush it. (00:27:25)
Deliberate mistake: The kid who falls into Niagara Falls spends 28 seconds falling before Superman catches him. Niagara Falls is 51 meters in total height. Considering how fast something falls, the kid should have hit the water long before Superman ever entered the scene. (00:39:30 - 00:40:00)
Revealing mistake: In a close-up shot of the kid falling into the falls, one can notice the kid is just a dummy. Notice how his face is a lot paler than it was before. (00:39:35)
Continuity mistake: Right after Clark reveals himself to Lois in Niagara Falls hotel room, by his hand falling into the fire, he backs up to where the bed and lava lamp like column is behind him. In that shot, there isn't much of the "lava" in the column. The scene cuts to a shot of Lois and then back to Clark and suddenly there is a lot of "lava" in the column. (00:53:05)
Revealing mistake: When the villains enter the oval office, the whole White House behind is a cheap set with painted columns, furniture, fixtures and switches (even the bullet holes are painted!). (01:16:29)
Revealing mistake: 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. (01:34:40)
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. (01:39:50)
Revealing mistake: The villains send cars flying through the air. This was achieved with detailed scale model cars in a scale model Metropolis. But in order to mimic the blown-away citizens they use cheap mannequins that move on some sort of conveyor belt. (01:43:50)
Revealing mistake: In the first scene when the villains are at the console, you can see Ursa's nose disappear, then reappear when Non walks behind her, then it disappears again. (01:44:30)
Revealing mistake: In Houston, when a man is thrown through a truck, notice the ground he falls on: The sand is leveled higher than the rest of the road around, obviously to hide a landing mat. Furthermore, after the fall the man turns around and he's got a bulgy square on the back to help for a safe stunt.
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.
Continuity mistake: When Superman starts playing hide and seek with the villains, he stands away from the icicles. When Ursa shows up a frame later, he's leaning against them.
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.
Revealing 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.
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.
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.
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.
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.
Answer: Superman was be able to kiss Lois in such a way that the heightened emotion wiped out her memory of his identity. To answer your second question, even though Lois promised not to tell anyone, Superman decided he does not want even her to know his secret identity.
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