Deliberate mistake: When the villains rampage the White House, the flag's base remains on the ceiling, and the flag pole falls inside the house. So the final scene with Superman carrying the flag and its base as if it had been previously stolen or destroyed, is nonsensical, but it looks very patriotic indeed.
Continuity mistake: In the Niagara falls, when Superman brings Lois a hot dog, the wider angle doesn't show a woman with a beige sweater coming form the right, who suddenly appears in the close up.
Revealing mistake: After Superman saves the kid at Niagara Falls, he lands on a lawn nearby. Then wires holding him are visible.
Continuity mistake: After Zod grabs the cop's rifle, a close-up shows the rifle's butt close to the policeman, which is inconsistent with the next shot where the villains are seen many meters away.
Continuity mistake: When Non lifts the cops' car, the fat cop starts to tuck his head inside the car, but a frame later it's already in, without having finished the movement.
Continuity mistake: In the big fight in Metropolis Ursa chokes Superman, but a frame later she is 3 meters away from him and her hands are off his neck.
Continuity mistake: When Superman brings the flag to the White House, the wide shot shows the wind stopping, and the flag coming to a smooth stop. Immediately after, in the close-up, the flag is moving wildly.
Continuity mistake: When Clark is lying beaten up on the diner floor, a man in a brown suit next to him disappears.
Continuity mistake: In the bar in East Houston, the man that challenges Ursa to arm-wrestle has his right arm and elbow on the table. In the next shot they're down.
Continuity mistake: When Ursa sits down to arm-wrestle, a man with a red jacket who was sitting several feet to the left, suddenly appears on the back close to the guy with a Coors T-shirt.
Continuity mistake: The watch on the left hand of the cop holding the binoculars while watching the Eiffel Tower, appears and disappears between shots.
Continuity mistake: When Ursa descends through the White House window, she is facing the back of the cop holding a gun. In the next shot she lands facing somewhere else, the cop now being by her side.
Continuity mistake: When Ursa grabs the snake, in the close-up her badge appears skewed. In the rest of the shots the badge appears straight.
Audio problem: Trapped under the elevator, Lois says "Capital P" but she is not mouthing the word.
Revealing mistake: When Zod takes the rifle out of the cop's hand the strings moving the rifle are seen, each by the side of the cop's cowboy hat when the rifle turns red.
Continuity mistake: The coat hanger in Perry's office disappears between shots.
Continuity mistake: Non smashes Perry's glass but a second later the glass is back in place.
Continuity mistake: In the Fortress of Solitude, when Non is (green screened) flying towards Superman, Ursa and Lois disappear.
Continuity mistake: When Clark and Lois land inside the ice cave, the wires holding her are visible.
Continuity mistake: Under the elevator when Lois says "Nobel prize" her fingers are completely black, covered in grease. When she starts to say "lil' o" they're just slightly dirty. When Superman saves her they're spotless.
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.
Matty Blast