Two big ones for me:
That NASA never actually landed on the moon. Okay...if not...why does it matter? What would be the purpose of faking it? To equal the Soviets? Yeah, maybe...but even then I still don't really understand the importance of it. I don't give a shit if we were there or not lol. It doesn't change anything in the course of history as far as I am concerned.
That Paul McCartney died in the 60's and secretly was replaced by a look-alike. Come on!