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, 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.
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: 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.
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.
Continuity mistake: After Zod launches Boog through the truck the cop asks if he's OK and he and the kid turn sideways an look at him. A shot later they are facing straight.
Continuity mistake: When Zod launches Boog through the cafe window, he lands a couple meters away from the cop, but a shot later he's at his feet.
Continuity mistake: When the movie begins Zod breaks the red glass and there's a brief shot of Ursa looking in fear. Her hair is longer than in the previous shot.
Continuity mistake: When the villains are trapped in the phantom zone (filmed by Richard Donner) Zod, Non and Ursa (from left to right) are tightly pressed against a glass. When the elevator explodes and are about to be released (filmed by Richard Lester) not only are they not pressed, but neither in line, having changed positions (and looks, as already listed): Non now stands above Zod and Ursa.
Continuity mistake: In Krypton when Non breaks the guard's neck the guard presses an emergency button. In the wide angle all of his fingers are extended, but in the close-up only the index is. This changes back and forth.
Continuity mistake: At the Fortress, when the 3 villains extend their arms to send a laser beam to Superman, there's a very brief shot on Ursa and her hair style is completely different. Very short and with her forehead very clear.
Continuity mistake: When Superman is putting the antenna back in place, watch the right of the platform with a bunch of metal parts and cables sparking. In the closeup they disappear.
Continuity mistake: The branch that Superman cuts to save Lois from drowning swaps from bright milky chocolate colour to pale dark brown depending on the shot.
Continuity mistake: In the balloon, after Luthor says "Due North", Teschmaker's arm swaps from raised to lowered.
Continuity mistake: When Lois is cutting oranges the glass jumps from being on the right side of the table to being on the far left.
Continuity mistake: When Superman is crossing the street and a taxi crashes against him, the passers-by are not continuous between shots. Check the African American girl in a pink dress who appears randomly on every single corner of the streets around.
Continuity mistake: After Lois asks the Paris spokesperson about the bomb he turns around and talks to her. Then it suddenly cuts to a closeup of his face and he's now talking to the journalists that were on the left, without having turned his head or body.
Continuity mistake: At the Eiffel Tower Lois approaches the spokesperson, cut to a wide angle where he is facing left. Then as she arrives there's a close up of him turning around. Then back to the previous wide angle where he is facing left again.
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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