Minor Plot hole: When the astronauts are commenting on the dropping temperature, they are at the Moon's southern pole, which is about -390 degrees F. They would not have been able to feel temperature fluctuations through their environmental suits.
Minor Plot hole: At the beginning of the movie it is stated that Apollo 17 landed on the moon on December 7, 1972. This is actually the launch date of that mission. Apollo 17 landed on December 11, 1972. Oops!
Minor Plot hole: During the whole film, there is no radio lag between earth and the lander or the orbiter, which is simply impossible.
Major Plot hole: The astronauts in this film are sent to the moon on a secret mission to place motion cameras to supposedly spot Russian missiles. Toward the end of the movie, the two astronauts on the moon realize the cameras are really there to monitor the alien moon spiders that live there (seriously). The question is, why was it necessary to lie to the crew about why they were going there?
It was already established that it was a secret mission, as they were not even allowed to tell their families they were going to the moon. Unlike the Alien films, the Department of Defense didn't seem to want to bring the creatures to Earth, since they ordered them NOT to return with a lander full of the things. The DoD could have just told the truth and gotten their highly trained astronauts and extremely expensive equipment back.
Super Plot hole: The film claims we've never gone back to the moon failing to explain how the found footage used to make the movie was retrieved in the first place. Did you hear that sound? It's your neurons committing suicide after realizing how intelligent the premise of this movie is.
Unaddressed Issue: The space spiders (or whatever) seem to be thriving on the moon, despite a lack of a regular food source. Despite the occasional astronaut or cosmonaut, the moon is not exactly teeming with wildlife. If they generally just eat rocks, then it would be unlikely that they would attack and eat (or at least infect with moon venom) a human, a life form they would have no way to be adapted to. So what's up with that? We have to concede we don't have enough neurons anymore to figure this one out.