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.
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.
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.
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