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)
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)
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: During the hide-and-seek sequence with the villains, multiple Supermans appear on screen simultaneously. Each of them is outlined by a faint black rectangle, revealing where the images were composited. (01:44:35)
Revealing mistake: 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.
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.
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.
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.
Revealing mistake: Near the end of the film when the 3 villains fly and later enter the fortress, you can see that it was a stuntman and not Gene Hackman.
Revealing mistake: In the New York battle scene, after Ursa distracts Superman, Non punches him and he goes flying backward into a building. Watch very carefully along the bottom of the screen. You can tell that Superman isn't even matted in from the chest down. Where is the rest of him?
Revealing mistake: 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.
Revealing mistake: 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.
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.
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: When Ursa kicks the astronaut into space, she takes a step back and looks upwards. When this happens you can tell that the film is being shown at double speed. Also, when Clark spins the guy on the chair at the end of the film, he snaps back upright far too quickly.
Revealing mistake: Inside the White House, Non throws a pillar at the soldiers. When it lands on the floor, it starts to move by itself like a puppet, revealing the whole structure was attached to a string.
Revealing mistake: The shot of people walking on the street by the Daily Planet is the same one used in Superman I.
Revealing mistake: The fire that comes out of the flame throwers moves at a slow speed though the scene is developing at normal speed.
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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