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.
Continuity mistake: In East Houston, after Ursa says "your general wishes to speak" a sudden change of light takes place and her face swaps from shady to very bright.
Continuity mistake: When the TV camera focuses on Zod, there's a man crouching by a car behind him. Half a second later he is standing and leaning on the hood.
Continuity mistake: In the Niagara falls, when Superman brings Lois a hot dog, the wider angle doesn't show a woman with a beige sweater coming form the right, who suddenly appears in the close up.
Continuity mistake: While Superman is crushing Zod's hand, there's a close-up of Non watching the scene in awe. In the following shot, Non's expression has changed to normal.
Continuity mistake: After Zod grabs the cop's rifle, a close-up shows the rifle's butt close to the policeman, which is inconsistent with the next shot where the villains are seen many meters away.
Continuity mistake: When Non lifts the cops' car, the fat cop starts to tuck his head inside the car, but a frame later it's already in, without having finished the movement.
Continuity mistake: In the big fight in Metropolis Ursa chokes Superman, but a frame later she is 3 meters away from him and her hands are off his neck.
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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