Three basic arguments that I have not yet seen thoroughly refuted:
If NASA can fake great acheivments, then why haven't they faked, say, a Mars landing?
Why didn't the USSR discredit the moon landing? They had the ability to track the lander in, and the command module back, and never said it was fake. They were mortal enemies of the US at the time, and refutation of the moon landing would have been a propaganda coup for the Soviets.
Why, when hundreds of thousands of people worked on the Apollo missions, has nobody ever said that it was fake? No scientist on their deathbed, no anonymous engineer, there are no credible sources of workers exposing it as fake.