Back on July 20, 1969 I remember staying up to watch this with my father. Here is a NASA Contractor Report on the flag raising. My father was not the most talkative man in the world, but I could tell he was quite proud when the flag was raised. So was I.
The flag raising has been seized upon by conspiracy theorists who claim that the moon landings were government hoaxes. How could a flag wave without an atmosphere? This has been answered numerous times.