Various things in the film not found or possible on the moon: desert vegetation; wood (torches, and the stake used to tie up victims in the spider cave); sound; a sunny, cloud-filled sky.
The "spacesuit" helmets leave the astronauts' skin exposed around their necks, which would of course be instantly fatal on the moon.
The bottom of the missile's entry hatch has no visible manual locking devices or latches like the top has yet the escaped convicts were locked inside.
On the way to the moon they passed through a "meterorite" field.
When the rocketship lands on the moon, the gantry and blockhouse seen in the take-off sequence on Earth are plainly visible (the result of running the stock footage of the V-2 launch used in the film in reverse).
In the blast-off sequence, cuts are made to stock footage of a World War II vintage German V2 rocket launch. The V2 looks nothing like the "ship" that was shown out the window, not to mention that the V2 launch was in broad daylight and "our" launch was at night.
The rocketship bottom used in the moon sequence is very clearly a cardboard cut-out.
When Dirk pulls back the curtains of his office window to reveal the moon rocket, it's obvious from the forced perspective that the rocket is a model placed just outside the window.
A line is plainly visible between the separate sections of the desert backdrop seen behind the police car, and later behind the spaceship. The two sections also don't fit together correctly, so that the scenery on them doesn't match properly.
Dirk dies aboard ship, but no indication is ever made of what they did with his body.
As Dirk dies, he says, "My Lido, forgive me." Later, still aboard the ship, Gary asks Steve, "Who was that dame he [Dirk] was talking about?" Dirk never mentioned who or what sex the "Lido" was, so Gary could not have known that the Lido was a woman while still en route to the moon.