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.
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.
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: 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.
Audio problem: In the prison, Lex tells an inmate he wants his Liberace record, to which he replies, "It has a scratch on it," but his lips don't match the audio. In the Donner version, it's revealed that the original audio was "Tonight?"
Continuity mistake: At the Fortress, when Lois drinks champagne, she holds the glass at chest level. A shot later, her arm is lowered.
Revealing mistake: When Non flies through the White House ceiling, right before he lands on his feet, the shot cuts to Zod landing safely and one can see that the previous stuntman missed the landing and fell on his back, his legs now pointing upwards. According to the shooting script and the additional Donner scenes, the fall was not scripted and not plot-wise.
Revealing mistake: When Superman returns the flag, the wide shots show he has really long arms and a brown blob where the head should be, revealing the actor has been replaced with a dummy.
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.
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