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)
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)
Continuity mistake: When the villains arrive at the Daily Planet, the furniture, decor, and buildings in the background change between shots.
Continuity mistake: After the Metropolis fight, the villains return to Perry's office. In the close-up, the whole background changes: the buildings, the debris around, and even a column and a broken blind appear behind Non.
Continuity mistake: At the Fortress, when Lois drinks champagne, she holds the glass at chest level. A shot later, her arm is lowered.
Continuity mistake: Before Non breaks the table in two, the phones are lying next to the edge. When he raises his fist, the phones are further away.
Continuity mistake: Right before Perry White throws a bronze globe at Non, Lois' head is tilted sideways and she smiles calmly. An instant cut later, her head is straight and she stares in awe. After the globe strikes Non's head, we're back to the previous shot where her head is tilted.
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.
Continuity mistake: In Niagara, Clark moves to the left to warn a kid from falling and a woman next to him lowers her camera. In next shot the camera is up and she repeats the previous movement.
Continuity mistake: Clark and Lois are undercover in a hotel in Niagara Falls investigating a Honeymoon scam. There is a scene where Clark is removing money from his pocket to tip a porter. You can plainly see that some of the money is falling on the ground. In the next scene the porter walks away with his tip and the falling money has disappeared.
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.)
Continuity mistake: The corner in the Fortress of Solitude that exploded looks totally different when we see it at the end of the film.
Continuity mistake: There must be a barber's shop or a cosmetics shop somewhere in the Phantom Zone. At the beginning of the first Superman film General Zod's hair looks as if it has been blow-dried, but all through Superman II he looks like he uses wet-look gel.
Continuity mistake: During the fight in Metropolis, General Zod is about to throw a wall part at Superman, it cuts to a street scene with people and there is a "no entry" sign reversed, showing the film was flipped for some reason.
Continuity mistake: When Ursa throws the White House cop out of the window on the ceiling, the hole in the glass appears before he goes through it.
Continuity mistake: When Lois is trapped under the elevator, the wide shots show a thick metal bar close to her throat. In the closeups showing her head and shoulders the bar isn't visible.
Continuity mistake: Superman stands on a flag pole outside one of the windows in Perry's office to defy the 3 villains. When the shot cuts to an outside view of the villains flying, the flag pole has disappeared, and the nearest one is several feet to the left.
Continuity mistake: When Luthor is at Perry's office door, his hair changes from long and messy to short and combed in the next shot.
Continuity mistake: When Lois is falling on the elevator, the camera angle cuts between her reactions and the ground coming up quickly. When Superman arrives to save her, there is suddenly a LOT more distance from the elevator to the ground than there was just a moment before.
Continuity mistake: Zod punches Superman and makes him fly backwards and crash against a metal structure. The wide shot shows him in the middle of it, but in the immediate close one, he is located on the right side.
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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