One common argument for the landings being faked is the whole "The LM was made of aluminum foil and tape!" thing. Here's some good counterarguments. "Well, the De Havilland Mosquito (a WWII airplane) was made out of balsa, and could fly at 400 mph. It's as true as the LM being made out of foil." (Posting a picture is good.) (Ironically, it's actually more true than LM was made out of foil bit. The Mosquito was effectively made out of what was in many ways an early version of composite materials, except using wood products, and IIRC, balsa was one of them.) Another good thing to point out is that foil like that is used extensively on satellites and planetary probes.
Even I was surprised to learn they used tape to attach the Kapton? foil. I would have assumed they would have glued it to the underlying structure. But it was explained to me quite well - what is tape, but a piece of material with glue on one side? That pretty much immediately led to an "ah, now I understand" moment. The tape is just a piece of material across a joint was glue on one side. Another thing to bring up is that the "foil" is just an outer covering to keep the sun off, and actually is somewhat flimsy. But then again, with no air resistance, it didn't need to be strong, The actual structure was underneath it, and was plenty strong enough. (Post a picture of a LM under construction without the outer covering attached.) Another point is that the actual cabin the astronauts were in was about the thickness of a beverage can. So, IIRC (I think) was the outside of a B-17.
One final good thing to do would be to turn the question around, and ask a HB what a lunar lander should look like, or how they would design one. Hopefully that would occasionally lead to a bit of thinking,
(PS: About the Kapton tape, would common duct tape have been strong enough for that application? Just something I recently wondered about.)