I understand there are two rival theories in FET concerning the shape of the moon : Spherical or discoidal. I used a 3D program (Softimage) to render images of what the moon would look like in both models.
I start from the hypothesis that the moon is 3000 miles above the earth, as claimed in your FAQ, that it's either a sphere or disc, and that its visible side or hemisphere is always pointing downwards. Let's consider an observer 3000 miles away from the point on earth below the moon. So the moon is seen from an angle of 45°. Let's see what it would look like in both models:
The result is that none of the two assumptions corresponds to everynight's observation. In the spherical model, we would see a large part of the far side of the moon (coloured blue for clarity); in the discoidal model, the moon would appear as an ellipse. Logic dictates that my initial assumption must be false. Thus, the moon is actually
not rotating 3000 miles above the ground, qed.
Again, observation disproves FET.
(As a sidenote, one might argue that the moon does not actually face downwards, but somehow turns towards the observer to keep its far side hidden and its shape nice and round. But then again, given that there are about seven billions of observers scattered all over the glo... errr disc, the moon would have a hard time turning towards all of them at the same time, wouldn't it?)