Deliberate mistake: The kid who falls into Niagara Falls spends 28 seconds falling before Superman catches him. Niagara Falls is 51 meters in total height. Considering how fast something falls, the kid should have hit the water long before Superman ever entered the scene. (00:39:30 - 00:40:00)
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.
Deliberate mistake: French officers and firemen speak in English between them.
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.
Matty Blast