I prefer to focus on the evidence moon hoaxers have presented.
By and large, it's not evidence. Most of it is argumentation of the form, "Normally you would expect X to be observed. We observe Y instead. Y can only be explained by some hoax theory. Therefore it was hoaxed."
The strength of that line of reasoning rests on the premises, "Normally you would expect X to be observed," and "Y can only be explained by some hoax theory."
Very few conspiracy theorists take the trouble to establish why "Normally you would expect X to be observed." That is, their claims of anomaly rest on their personal expectation. If you're going to define an anomaly by measurement against an expectation, then the objective strength of that expectation is essential to the argument. If the expectation is instead simplistic or based on a few isolated observations, then it cannot be used as a yardstick against which to define an anomaly.
And the premise, "Y can only be explained by some hoax theory," is usually established only by elimination. That is, the conspiracist identifies a few token potential causes that are shown
not to produce Y, and therefore by some purported process of elimination he claims to have shown that the "only" remaining explanation is some sort of hoax. That fails for two reasons. First, if you plan to prove something indirectly then you bear the burden of proof to show that your examination was exhaustive and appropriately falsificatory. You can't stop at a few straw men. You can't skimp on the falsification. Second, proof by elimination is unsatisfying if no direct, positive evidence substantiates your claim and it would otherwise be expected. That is especially true when the claim is extraordinary. "Proving" some farfetched claim indirectly is a weak argument.
So here's a typical Jack White claim.
http://www.clavius.org/bigmt.html
Fitting it to our syllogistic framework we have, "In real photography we expect the depicted distant objects to be the same size. Here they aren't. Photographer movement does not account for that change in size, so it has to be the result of some nearby backdrop or botched cut-and-paste."
The premise of equal size holds only if certain photogrammetric controls are applied. Not only did White fail to apply them, he specifically
defeated the controls that were handed to him on a silver platter. The Apollo lunar surface photography includes a reseau grid which is specifically used to normalize photograph size and correct distortion.
Of course the movement of the photographer can't account for the apparent change in size. No one is arguing that it does in this case. That's just the straw man White throws out there so that he has something against which to contrast his own conclusion.
In rushing to his desired conclusion, he has omitted the actual explanation: the difference in size is due
entirely to his mishandling of the images. He has cropped the pictures and resized one of them, making its mountain appear bigger. Historically, the crop-and-resize trick is one that White has used repeatedly. I have witnessed for 7 years people telling him how and why this cannot be done without violating the premises of his arguments, but he is impervious to it. That is, however, why the "anomaly" appears.
And White offers absolutely no confirmatory evidence of a backdrop or of photo doctoring. He merely dresses up a circular argument with the illusion of rigor. Evidence of a backdrop would include observations that can
only come from a backdrop. (For example, the exploding-Krypton scene in
Superman where the black velvet drape can be seen in the explosion element.) Evidence of photo composition would be evidence that can
only be explained by composition -- e.g., vast differences in optical density across the composition boundary, or discontinuity from negative-trimming. Instead White merely reverses the implication.
His approach on this point is logically wrong. It's methodologically wrong. It arrives at the "hoax" conclusion only because White fixed the evidence so it would. How does this not justify rejecting the claim?