One key piece of third-party evidence comes from the retroreflectors left on the Moon by three of the Apollo missions (11, 14, and 15) and by two uncrewed Soviet lunar landers. These retroreflectors have been pinged from dozens of sites all over the world; they are exactly where the US and the Soviet Union said their vehicles landed. The existence of the retroreflectors does not prove that the three US missions were crewed, but it does prove that some kind of landings occurred at those three sites.
The above points show that the Apollo program could have been taken place, and that there's lots of evidence that shows that it did take place. Could it have been fake? This leads us to ...
##5. The technology needed to fake the Moon landings did not exist at that time.
The Apollo astronauts took an abundance of photographs during their short stays on the Moon. The photographic evidence is very compelling, which compels the conspiracy theorists to try to debunk those photographs. These efforts inevitably fail; the lighting in every single photograph taken from the surface of the Moon is consistent with a bright light source one astronomical unit away and is inconsistent with studio lighting.
Those photographs could of course have been created as computer-generated imagery. CGI has recently been used to recreate some of the iconic photographs taken from the Moon. One of the two photographs below was taken by Neil Armstrong. The other is pure fantasy, generated by a computer.
The technology needed to produce those photographs as computer-generated images is very new (late 2014, to be precise), and even then, it wasn't easy. Such technology did not exist twenty years ago, let alone fifty years ago.