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.
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.
Factual error: When the Krypton criminals are on the moon, they speak both to each other and the astronauts, something that's impossible to do in space where there's no sound.
Factual error: When the police car's light is thrown at the boy and it blows up, it shouldn't have happened. The most that would've happened was that the kid would've been knocked off his bike when hit with the light. There is no explosive device in the light, so it shouldn't have exploded in the least like it did.
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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