Clementine's brother died with his spacesuit on whilst on the lunar surface. In such a sterile environment, with no oxygen present to fuel microorganisms, he should not have been reduced to a skeleton.
At the end of the opening credits the two astronauts are dumped into the "Capernicus Garbage Dump>" Assuming it was named after the famous astronomer and mathematician, the correct spelling would be Copernicus.
When Clementine tries to contact her brother by radio from the bug on the drive out to his claim, there is static hiss from the radio when she's transmitting and silence when receiving. In reality, it should have been the reverse: silence during transmission and static during reception.
If you fired a compressed gas based projectile on a low gravity environment such the lunar surface, or a zero gravity environment such as in space the recoil would send you moving backwards unless you were well and truly dug in, in which case your body would be forced to absorb the recoil. Yet whenever a gun is fired in this film the person who fires it remains static.
When Clementine discovers the skeleton of her brother, a suture line can clearly be seen separating the top half of the skull above the brow showing it to be a skull with a removable top.
When Capt. Kemp and Miss Taplin are bulldozing a shortcut to get back to Moon City in a moon rover, you can clearly see it's really a miniature vehicle being pulled by a thin string.
In a number of the exterior shots on the moon there are multiple lights reflected off the actors' suits, even though there should only be one light source (the sun).
When Kemp shoots the bad guy in the yellow spacesuit at the mining site, the puncture blows out on the top rear of his tank, yet leaves no hole in his front- despite the fact the bad guy is far above and facing him.
In the animated opening credits sequence, the name of producer Michael Carreras is incorrectly written as "Carerras".
Weightlessness and low gravity in this film is shown by slowing down people's movements. However liquid in glasses and Clem Taplin's long hair is never affected.