Other mistake: When Lois and Clark leave the Fortress, the car is driving in the wrong lane. This is due to the fact that the shot belongs to a reused scene from the first movie, where an empty car was remotely driven by Lex, who changed lanes all the time.
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.
Revealing mistake: All of the movements of both people and objects on the moon are played in slower speed to simulate the Moon's gravity, except for the last scene where Zod grabs the oxygen tube and it falls on the ground at normal speed.
Continuity mistake: When the villains arrive at the Daily Planet, Lois grabs the telephone. An instant later, it has vanished from her hand.
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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