Continuity mistake: When they are in east Houston, Idaho, the helicopter gets knocked out of the air and lands upside down onto a jeep. You see the pilot get smashed into the seat of the jeep real hard and yet seconds later he walks away unharmed.
Continuity mistake: Inside the bar in East Houston, Zod pushes a man backwards, but the next shot shows the man flying as if he had been thrown upwards.
Continuity mistake: When Superman falls on the Marlboro truck, the part reading "Ma" gets more crumpled after Superman leaves the truck compared to when he landed on it.
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: At the Fortress, when Lois drinks champagne, she holds the glass at chest level. A shot later, her arm is lowered.
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.
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: Inside the White House the cops fire 3 or 4 times at Zod but the wall and statue behind him have at least 15 bullet holes.
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.
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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