Continuity mistake: When Ursa throws the sewer lid to Superman, first she is standing in the middle of the street but in the next shot she is close to the curb, by a yellow cab.
Continuity mistake: When the News Beat reporter arrives, the shadow on the satellite dish changes significantly in a couple of seconds.
Revealing mistake: Near the end when Zod and his crew are blowing everybody away, there is a shot of two cars going into a department store and one flying right to left. There are also two "people" running away in this shot. They're dummies. One of the cars hits the person and he wobbles. Incredibly obvious. These aren't mannequins from the store either; they're on a track and follow a path from right to left.
Revealing mistake: When Zod picks up the guy in East Houston, you can see right through the guy. He's transparent.
Continuity mistake: When the cab hits Clark, an African-American woman in pink is crossing the street. In the next shot, she’s suddenly several metres behind, handing money to a woman with a donation box. A moment later, she’s shown walking toward the charity woman again from a distance.
Revealing mistake: When Superman is saying, "No, don't do it! The people!" you can see Christopher Reeve is trying his hardest not to laugh.
Visible crew/equipment: When Non smashes a glass window at the Daily Planet, everyone ducks, except for Lois, Perry, and Jimmy. However, there's someone in front of Non reflected in the glass, all calm, watching the havoc, wearing a dark jacket and a white shirt with his arms crossed, seemingly a crew member.
Continuity mistake: Lex sits in the President's chair and lights up a cigar. A shot later, it has swapped hands.
Continuity mistake: When the villains enter the Oval Office, there's a civilian in a blue suit on the right. In the aerial angle, he is stepping on the hardwood floor, but in the wide angles, he steps on the rug. This swaps back and forth.
Continuity mistake: When the villains arrive at the Daily Planet, Lois grabs the telephone. An instant later, it has vanished from her hand.
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.
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, 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: 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.
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.
Continuity mistake: When Zod is interviewed by the news reporter the people behind him differ or change positions between shots.
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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