Yes, to add to the other points - they brought back rocks from the Moon - and each rock was labelled so you can tell where it was picked up and when. And they lead to new and surprising discoveries about the Moon. And these rocks are used to this day, re-examined to test theories and ideas.

GEOLOGIST'S FIELD TRIP ON THE MOON

I'm talking mainly about Apollo 17 here as the one with the most interesting rocks returned, because returned by a geologist. But if you are doubtful about Apollo 11 you will surely be even more skeptical about Apollo 17.

You can watch the video of his expedition and share his excitement as a geologist as he made new discoveries on the Moon every hour.

Remember - every time he picks up a rock sample there - as a researcher you can go and ask to see that very sample and analyse it and test it to check or confirm theories about the lunar surface.

And that the rocks you can go and see - they look exactly as expected from the videos -same shape, same composition, if they pick up orange soil, they return orange soil, if they pick up a strangely shaped rock, they return a rock of exactly that shape...

Especially when you also read about Harrison Schmidt's field trip, here A Field Trip to the Moon - and more detailed accounts elsewhere, the discoveries they made.

How could they fake rocks to give the right results in experiments that would be done decades later using instruments not yet invented at the time, and to give reasonable results when used to test scientific theories about the Moon that nobody had thought of back then?

And all the time also be appropriate rocks for the locations they were found in the videos taken way back then of the astronauts actually picking them up?

EXAMPLE OF AN INTERESTING LUNAR ROCK STUDIED WITH TWENTY FIRST CENTURY INSTRUMENTS

For instance this one

Troctolite 76535

Studied for instance in this 2009 paper examining isotope ratios and giving new results about the moon Early Lunar Magnetism

Do you think they anticipated that some time in 2009 someone would examine this rock and want to find out the isotope ratios of Argon and manipulated them to make them appropriate for a hyopthesis not even thought of at the time? And designed the film to make everything fit together seamlessly to fit those ideas?

MICROMETEORITE DAMAGE

And then - to somehow simulated micro-meteorite damage and spherules in all the lunar samples so that even when looked at with electron microscopes they still look like lunar rocks?

Spherule with micrometeorite damage in lunar rocks.

We don't get micrometeorites on Earth, because they burn up in the atmosphere, while the lunar rocks are damaged in this way. This is an immediate give away that the rocks come from somewhere in space, where they have been exposed to micrometeorites for billions of years.

Even today we wouldn't have the technology to simulate this damage on all the samples, so they would stand up to electron microscope scrutiny.

The rocks are similar to Earth rocks, true - that was a surprise, how similar they are, and lead to the theory that the Moon was formed by an impact with the Earth.

But not identical. One obvious difference is that they all had micro-meteorite impacts which Earth rocks don't have. At a level you can explore with the electron microscope - no way that could be simulated in 1960s. I don't think we could do it convincingly today - might spend millions of dollars trying to simulate a gram of lunar rock so that a randomly selected sample would look right in an electron microscope, and fail.

COMPOSITION OF THE ROCKS

Also they were very very dry, lacking in volatiles and not hydrated like their Earth counterparts. And many are as old as 4.5 billion years old, older than any Earth rocks. See Moon rock

And the rocks match the rocks that the astronauts can be seen picking up on the Moon in the videos, same shape, exactly the right material etc. to match the place they pick it up in the lunar surface.

Or if you think unmanned rovers on the Moon brought the rocks back - how do they exactly match the rocks the astronauts pick up in the videos?

Also, not just returned by US astronauts.

The Russian Luna program returned a total of 0.326 kg in all their missions to the Moon, which confirms what's been found in the Apollo rocks.

The rocks don't match any other rocks from Earth, or outer space.

We now have Lunar meteorites which we can recognize because they match the composition of the lunar rocks.

Here is a comment by an expert on lunar meteorites:

"Any geoscientist (and there have been thousands from all over the world) who has studied lunar samples knows that anyone who thinks the Apollo lunar samples were created on Earth as part of government conspiracy doesn't know much about rocks. The Apollo samples are just too good. They tell a self-consistent story with a complexly interwoven plot that's better than any story any conspirator could have conceived. I've studied lunar rocks and soils for 40+ years and I couldn't make even a poor imitation of a lunar breccia, lunar soil, or a mare basalt in the lab. And with all due respect to my clever colleagues in government labs, no one in "the Government" could do it either, even now that we know what lunar rocks are like. Lunar samples show evidence of formation in an extremely dry environment with essentially no free oxygen and little gravity. Some have impact craters on the surface and many display evidence for a suite of unanticipated and complicated effects associated with large and small meteorite impacts. Lunar rocks and soil contain gases (hydrogen, helium, nitrogen, neon, argon, krypton, and xenon) derived from the solar wind with isotope ratios different than Earth forms of the same gases. They contain crystal damage from cosmic rays. Lunar igneous rocks have crystallization ages, determined by techniques involving radioisotopes, that are older than any known Earth rocks. (Anyone who figures out how to fake that is worthy of a Nobel Prize.) It was easier and cheaper to go to the Moon and bring back some rocks then it would have been to create all these fascinating features on Earth."

See How Do We Know That It's a Rock from the Moon?

TRACKING BY INDEPENDENT OBSERVERS

The Apollo 11 mission, as for the other missions, was tracked by professional astronomers and keen amateurs (reported in Sky at Night magazine) on its way to the Moon.

See Telescopic Tracking of the Apollo Lunar Missions

Also the Jodrell bank telescope tracked it along with all the other space missions on its way to the Moon, with such precision, that using doppler shift of the signal they could see in their recordings where Neil Armstrong took over with manual control during descent to the lunar surface.

Referred to here: Jodrell Bank stories - I'll try to find a better link to it.

They also simultaneously tracked the Luna 15 attempt by Russia to return a sample from the Moon which crashed somewhere in the sea of tranquility.

You can listen to the recording of them as they tracked Lunar 15, with the sound of the Apollo astronauts in the background in the broadcasts they picked up from the Moon here: Jodrell Bank Centre for Astrophysics

For more about this, see Third-party evidence for Apollo Moon landings (Wikipedia)

SIMULATING WALKING ON THE MOON

And do you think they really managed to simulate Apollo astronauts walking on the Moon to look real, to this day?

When the most sophisticated movie about the Moon done before the landing was 2001, the year before - where this is their best footage they managed, after five years of work on the film, for the lunar sequence:

I can tell you the film was pretty amazing to watch at the time. We didn't know any better. It came out in 1968, the year before Apollo 11 landed on the Moon.

But look at it today - and is obvious those astronauts are just walking slowly, doesn't even resemble the lunar walking on the Moon.

Even today, our movies of astronauts on the Moon surface are not convincing for those who watched the Apollo landings. For instance on the "Apollo 18" movie - looks nothing like the real thing, just walking slowly basically.

I think myself, the only way to do it reasonably convincingly, even today - apart from microgravity flights and film everything in planes 20 seconds at a time - is something like this

From the NASA Archive: The Lunar Walking Problem | Science | WIRED

Which NASA did have in the 1960s - but - I've never seen anyone suggest they used this - and - how could you anyway - attach wires to absolutely everything that moves (including flag etc).

In a Mythbusters episode they looked at the idea that the moon walking could be done by slow motion video, and showed that it didn't look exactly like the lunar footage + other tests of moon conspiracy ideas. Episode 104: NASA Moon Landing

Here is another take on the whole thing by a movie director:

Writer/director S G Collins of Postwar Media debunks every theory that the Apollo Moon landings could have been faked in a studio. The filmmaker takes a look at the video technology of the late 1960's, showing alleged fraud was simply not possible.

And you can now see photographs of the tracks they made on the Moon, taken from orbit.

It's not only harder to fake than to do it. It's literally impossible to fake, not without ability to look into the future and have technology not yet invented and know about future scientific theories and instruments not yet invented.

MITCHELL AND WEBB SKETCH

See also The Great Moon Hoax - and the other answers on this page are great :).

PROFESSIONAL CALM OF THE ASTRONAUTS

Actually I wonder if part of it was because most of the astronauts were so professional about it and calm. They don't really seem like people doing things for the first time ever perhaps. Maybe it looks as if they can't be in any danger because they are so very calm?

But remember these are people who are professionally trained to be calm in the middle of a crisis in a jet fighter which is about to crash. It takes years of training to be as steady and calm as that - you and I could never do it without that training (unless you are in a similar profession).

We've seen so many movies of things like this and the actors in the movies are so much more excited by things and scared by them (even though it is acted) than the lunar astronauts seemed to be, and convey that excitement and fear to the audience well. Perhaps, paradoxically, if we'd sent actors to the Moon they would have been more convincing to the skeptics :).

On that first landing on the Moon especially - though they had done everything they could to make it safe - there was certainly a real risk that they would crash (even through momentary pilot error) and a significant risk that once landed, they would not be able to leave the Moon again but would die there or crash on take off. And they all knew that. The US had even prepared a speech for the president to say in the event that the Apollo 11 astronauts landed, and could not take off from the Moon again.

Here it is

What if the moon landings had failed? The poignant and moving speech that President Nixon would have delivered if Apollo 11 astronauts had not come home

But you'd never guess that they knew that from the way they talked.

Here is Neil Armstrong narrating the video of their landing, done in parallel with Google Moon