Audio problem: At the Eiffel Tower, after Lois asks the French officer if the terrorists have the proper equipment, his voice is heard but from a side view his mouth and jaw don't move.
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.
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.
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.
Continuity mistake: When the cab hits Clark, an African-American woman in pink is crossing the street. In the next shot, she’s suddenly several metres behind, handing money to a woman with a donation box. A moment later, she’s shown walking toward the charity woman again from a distance.
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, the fall was not scripted and not plot-wise.
Revealing mistake: When Luthor is about to climb up the balloon his bald cap wrinkles by his nape.
Revealing mistake: In the prison laundry, Luthor's bald cap is very noticeable, especially by his sideburns.
Other mistake: The phantom zone villains were captured and put in space near Krypton. When Kal-El was sent to Earth, he has to pass 6 galaxies to arrive (his father said, before Krypton exploded). When Superman sends the hydrogen bomb in Paris into space, he didn't even leave the solar system. No way the phantom zone travelled through 6 galaxies - it has no propulsion, and the shock wave from the bomb wouldn't travel that far either.
Revealing mistake: During the hide-and-seek sequence with the villains, multiple Supermans appear on screen simultaneously. Each of them is outlined by a faint black rectangle, revealing where the images were composited. (01:44:35)
Continuity mistake: After Superman crushes Zod's hand, his hair gets wet and the fringe appears combed as a toupee.
Continuity mistake: When Ursa is moving the helicopter around, the sky keeps changing from sunny to cloudy.
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.
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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