Continuity mistake: When Non grabs Superman from behind, Supermans hands are down to his sides. When Ursa comes to hit Superman with the flagpole, Superman's hands are now up by his chest and under Nons grip.
Continuity mistake: When Clark walks down to the river to help Lois get out of the water, he falls on the water and she is swimming 4 meters away. When the angle cuts she is half a meter away.
Continuity mistake: The log that Clark cuts to save Lois from drowning changes style between shots.
Continuity mistake: Non enters Perry's office and kicks a plant which makes the coat hanger next to it wiggle, but not fall. When the angle changes, about a frame later, it is on the floor, several feet away from the first position.
Continuity mistake: Superman is putting the antenna back on the Empire State. first its base is brightly lightened, despite the antenna being on top. When he is about to anchor it, a split second afterwards, the base is totally dark.
Continuity mistake: After Superman holds the antenna falling on the woman's pram, in a matter of 3 seconds the parked cars she was standing in between (a yellow cab and a black car) come much closer together.
Continuity mistake: Lois is in the diner and the waiter serves her a Coke and leaves. Angle changes, the bad guy sits next to her and the waiter appears serving the Coke again. In the next shot, the angle changes again and he disappears.
Continuity mistake: In the diner, whilst Clark is asking the bad guy to step outside, the waiter is leaning over the baddie's right shoulder. When the angle changes he is leaning on the left shoulder.
Continuity mistake: Atop the Eiffel tower the climate keeps changing from sunny to cloudy within seconds depending on the angle.
Continuity mistake: Zod throws the Sheriff's rifle away and it lands next to the wheel. When the angle changes it has moved behind the wheel.
Continuity mistake: When Lois is making an orange juice the position of the oranges differs between wide and close shots.
Continuity mistake: After Superman crushes Zod's hand, his hair gets wet and the fringe appears combed as a toupee.
Continuity mistake: During the scene where villains arrive to the Daily Planet, Jimmy Olsen's haircut changes from long to very short.
Continuity mistake: When Clark comes back to the diner to take revenge, a dish next to the bad guy suddenly appears.
Continuity mistake: When Super arrives at the Daily Planet to defy the 3 villains, the outside shot shows three piles of books lined along the window. From the inside, all of the books are piled to the right. Also, the number of trophies on the bookshelf on the right, and the type and number of books changes between shots.
Continuity mistake: At the end of the movie, in the diner, the bad guy's food keeps changing appearance.
Continuity mistake: When Superman reveals his identity to Lois, the liquid in the top of the lava lamp changes from filled to empty in half a second.
Continuity mistake: After Superman throws Zod against the ice wall, Non's position changes between shots: First he is way behind Luthor, and a second later both are side by side.
Continuity mistake: When Non enters the Daily Planet there's a wood shelf with four sheets of paper, the ones in the middle are yellow and the rest are black and white. When the shot changes to a wide angle, all the papers are black and white.
Continuity mistake: When Ursa sits down to arm wrestle, coasters magically appear on the table.
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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