Watching the wierd way the flag that they planted flew, the way the dust dropped back to the surface after they kicked it up, and the speed of the pendulum they put in front of the camera convinced me that they were where they said they were.
By the way, I don't believe they had a video camera with them. The 1969-vintage video camera was a bit heavy for inclusion aboard the Apollo.
This first two missions (11 and 12) used black and white video cameras. The one used for 12 was burned out after a few minutes when one of the astronauts (Conrad or Bean, don't remember which) accidentally pointed it at the sun. The one on 13 was never used because that one never landed. Starting with Apollo 14 (Alan Shepard's mission) the cameras were color. By the time we got to the last mission, Apollo 17, the cameras were dramatically improved, providing quality nearly as good as the images you saw on the evening news every night.