When the colonel locks Ava in medical, his key card is required to open the door. The doctor takes it so he can get in while the colonel is medicated. Later, when the two of them return to medical, the colonel is able to enter without his key card.
In the beginning of the movie, at 02:24, Christian Slater's character activates some kind of 'communicator' and speaks into it. This is actually nothing more than a simple LED reading light.
Meteors only occur in the Earth's atmosphere. They would be meteoroids when impacting The Moon. Also there would be no sound from the impacts because sound needs something more than a vacuum in order to travel.
The very first lines are from a computer alerting of an incoming storm. This is impossible: the Moon does not have an atmosphere for storms (or any other weather phenomenon, in fact) to occur, and the resulting meteor shower does not count as one. However, meteor showers are often also called meteor storms.
At one point, they state that a sensor shows levels of carbon monoxide that are off the chart. However, the sensor indicates CO2, which is carbon dioxide; the abbreviation for carbon monoxide is CO.