Plot hole: Lois and a friend of hers are watching Non and Superman fight. But this is totally senseless, because Superman had been flying around Metropolis and chances are slim that he appears in the very same spot to let Lois watch him. And, second and most important, should any doubts arise, the panning angles of the camera never show Lois's building, with the big broken window and the flag poles.
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.
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: 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.
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.
Factual error: The moon has no atmosphere. Yet, the Ursa and Zod are able to speak to the astronauts. We even hear wind as Zod kicks one of the astronauts in the air and snaps his cord. We also hear the explosions when the lunar lander is destroyed. If the moon has no atmosphere, then the super villains can't speak and there should have been no sound in this part of the movie.
Visible crew/equipment: Lighting focus reflected on the cosmonaut's visor.
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.
Revealing mistake: Wires holding Superman are seen when he lands on the island to pick up fruit.
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.
Other mistake: When Ursa, Non and Zod first arrive on earth, watch out for the horrible lipstick marks on Ursa's teeth as they walk away from the lake.
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.
Revealing mistake: The fire that comes out of the flame throwers moves at a slow speed though the scene is developing at normal speed.
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.
Deliberate mistake: When the villains rampage the White House, the flag's base remains on the ceiling, and the flag pole falls inside the house. So the final scene with Superman carrying the flag and its base as if it had been previously stolen or destroyed, is nonsensical, but it looks very patriotic indeed.
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.
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.
Matty Blast