Factual error: When Nate dies by the alien moon rocks, his helmet visor "explodes." The visor in the film shatters like glass, but the real visors on actual spacesuits are made of polycarbonate, a plastic that does not shatter but deforms.
Factual error: During the first EVA, or extra vehicular activity, the two astronauts collect samples near an impact crater on the lunar surface. As the Lunar Module Pilot inspects the first sample, look carefully at his glove. It appears very flaccid and full of wrinkles. Anyone who knows anything about the suits worn on the moon knows they were pressurized. In a pressurized glove, we would not see wrinkles and flaccidity.
Factual error: Towards the end, as the Lunar Module pilot crawls out of the crater infested with alien spiders, we see visible clouds of dust when he moves around. The moon has a low enough atmosphere to be considered a vacuum. It is physically impossible for billowing clouds of dust (created by air resistance) to form in an airless environment.
Factual error: If you watch the scenes taking place in the lunar lander throughout the film, you'll notice that various objects fall as though there were a gravitational pull such as that on Earth, for instance, when a moon rock sample is dropped into a bag, or when a helmet falls on one of the astronauts while he is sleeping.