Continuity mistake: When the villains arrive at the Daily Planet, Lois grabs the telephone. An instant later, it has vanished from her hand.
Revealing mistake: In Houston, when a man is thrown through a truck, notice the ground he falls on: The sand is leveled higher than the rest of the road around, obviously to hide a landing mat. Furthermore, after the fall the man turns around and he's got a bulgy square on the back to help for a safe stunt.
Visible crew/equipment: Ursa throws the sewer lid at Superman sending him flying backwards into the car windshield. Watch the sewer lid carefully when Superman actually hits the windshield. You can see that the sewer lid was actually attached to a belt around his waist so that it would stay in place for the shots where he is flying backward through the air. (01:39:50)
Revealing mistake: When Zod lifts the boy's father with the beam of white energy, watch closely when he raises him up past the telephone pole...he 'clips' right through it, or rather the pole clips through him, as if he is transparent.
Visible crew/equipment: When Superman is fighting Non under the New York Streets (in the sewers), manhole covers start to jet up in the sky. When the first manhole cover shoots up you can quite clearly see the gas tube in the hole and the gas cylinder attached to the cover.
Revealing mistake: There are two external White House shots in the film. The second is a still shot, and should take place at least a few days after the first. However, it is a frame from the earlier shot, with the same person standing in the same spot on the lawn.
Visible crew/equipment: In the shot where Zod walks on the lake's water, there is a platform visible just under the water's surface.
Continuity mistake: During the fight in Metropolis, General Zod is about to throw a wall part at Superman, it cuts to a street scene with people and there is a "no entry" sign reversed, showing the film was flipped for some reason.
Revealing mistake: When Zod is thrown by Superman and passes by Luthor, the stand in is a guy with fluffy hair who looks nothing like Lex.
Trivia: When Clark and Lois arrive at the diner, Superman I director (and part of II) Richard Donner is walking by. He was fired before filming ended and was replaced by Richard Lester, but his cameo made it to the final cut.
Revealing mistake: After the Marlboro truck scene, Superman throws Zod and he goes through an office window. The harness to make him fly is visible on his back.
Continuity mistake: Before the villains arrive at the Daily Planet, Lois' hair is fluffy and her fringe has a straight cut. When the scene ends, her hair is shorter, and her fringe has some stylish cuts. Also, Jimmy's hair alternates between very short and long, due to Richard Lester's reshoots.
Other mistake: When Lois and Clark leave the Fortress, the car is driving in the wrong lane. This is due to the fact that the shot belongs to a reused scene from the first movie, where an empty car was remotely driven by Lex, who changed lanes all the time.
Other mistake: In the long shot of the Niagara Falls scene, the kid's right arm is way too long.
Revealing mistake: The 3 villains break through the Daily Planet window and fly around the city. Before Zod stops by a beam, Non becomes transparent.
Continuity mistake: After Non smashes Superman against a metal structure which gets totally crumpled, Superman stands up and the structure is undamaged.
Revealing mistake: Near the end of the film when the 3 villains fly and later enter the fortress, you can see that it was a stuntman and not Gene Hackman.
Revealing mistake: During the big fight in Metropolis, the close-up of the pram shows its empty or with blatant bundled pieces of fabric to simulate some sort of baby.
Visible crew/equipment: When Non crashes Perry against the ceiling, a crew member's hand is seen holding Perry.
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.
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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