Continuity mistake: When the News Beat reporter arrives, the shadow on the satellite dish changes significantly in a couple of seconds.
Continuity mistake: When the elevator falls down the shaft with Lois trapped underneath, Superman flies up to rescue her. He stops the elevator, and when he does, Lois climbs off from the bottom of the elevator and runs to hug him. Problem is, when she climbed off the bottom of the elevator, there should have been nothing but air underneath her.
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 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: 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.
Continuity mistake: When Lois comes out of the river she turns to the left to help Clark. Shot changes and she has turned 180ยบ around.
Revealing mistake: When Superman returns the flag to the White House, not only has the shot been reused, but the trees have been badly cut around to change the previous grey sky for a bright, blue and sunny one.
Revealing mistake: When Non burns the side of the cargo bed of the truck, a rectangular spot around the planks is coloured in a lighter shade, giving away where the special FX were placed.
Revealing mistake: When Superman flies towards the White House, in the close-up his cape and flag flutter at a normal speed, but in the wide shot they move really fast, quite comically actually, revealing that the scene has been speeded-up.
Other mistake: When Clark and Lois return from the Fortress of Solitude in a green car, the footage is the exact same one used in Superman I when Luthor later crashed that very same car (time code for Superman I 1:34:04 vs 1:18:25 for Superman II).
Continuity mistake: While in the water, Lois grabs the log with her right hand. A shot later she is away from the log and she grabs it again, though now she uses her left hand.
Revealing mistake: When Lois jumps in the river, she is replaced by a very obvious mannequin that floats stiff. Furthermore, the current tilts the dummy and its two arms bent like a sex doll's are perfectly visible.
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