Continuity mistake: In East Houston, behind the man lifted by Zod, there's a man standing several feet away from a car. A frame later he's very close to the car.
Continuity mistake: When Zod burns several cars, the street is filled with parked cars and people. From Superman's point of view the street is empty and you only get to see the three burning cars and a couple of cabs.
Continuity mistake: When the antenna is about to crush the pram, the mother is first behind it. A second later she's by the side. Then a second later she's on top of it, and a second afterwards slightly covering it. Boy she moves FAST.
Continuity mistake: Inside the Fortress of Solitude, when Non jumps to fight Superman, before he flies, Ursa and Lois are looking at Superman. A mere frame later, when Non starts to fly, both girls are in a different position fighting against each other. It's a really awkward and sudden change.
Continuity mistake: At the end, in the Fortress of Solitude, Lois' hairstyle keeps changing from fluffy and dull to smooth and stylish.
Continuity mistake: After the hide and seek game in the ice cave, Luthor's fringe constantly changes length and style.
Audio problem: When the villains blow the people back in Metropolis, all the ones near the KFC restaurant (the waitress, the guy in the phone booth and the couple) shout or make comments but their mouths either don't move or are not in synch.
Continuity mistake: Clark steps out of the diner and the waiter has his hands on his chest. A shot later his hands are on the counter.
Continuity mistake: After being hit by a cab, Lois calls Clark and the people behind her change in a split second.
Continuity mistake: When Ursa is moving the helicopter around, the sky keeps changing from sunny to cloudy.
Continuity mistake: In the big fight scene in Metropolis, after Ursa chokes Superman, Non descends and wires holding him is visible.
Revealing mistake: When Zod and Ursa jump out of Perry's window they fall down, revealing its a stunt from a ground level window. The outside shots however, show them flying up and straight.
Deliberate mistake: Luthor and Teschmaker visit the North Pole protecting themselves against the cold. Lois manages to wander around with a mere, but sexy, shirt.
Continuity mistake: When Superman is about to stop the elevator, he flies with one arm up the other down. A frame later in a new angle both arms are up.
Continuity mistake: On Krypton, when the guard gets caught, Non's hand is at chest level. In the close-up it is at belly level.
Revealing mistake: Before the villains change the faces on Mt. Rushmore, the original ones (which are a matte painting) have a greenish look. Definitely not like the real sculptures.
Revealing mistake: At the beginning of the movie, we see the three villains in front of several backgrounds. In most of these backgrounds, their outlines are fuzzy, indicating that they are actually standing in front of a green screen.
Visible crew/equipment: When the super baddies arrive on the moon and encounter the astronauts, the girl Kryptonian kicks one of the astronauts into space and you can see the strings around his waist as he floats away.
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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