Work on the Soviet Lunar L3 program was cancelled late in 1974. The LK ('Lunniy korabl' - lunar craft) was not revealed to the west until much later. Thus, the Apollo 18 crew would have had no knowledge of this vehicle (i.e. referring to it as the "LK").
Quindar tones (the famous "beeps" that are heard during radio voice transmissions from Houston) are heard in the film. However, the actual Quindar tones of Apollo were only audible to Earth-based listeners of the transmissions; astronauts did not hear the tones.
It would not have been possible for the Apollo spacecraft to land on the moon's south pole. Doing so would have required far more fuel, in order to move the vehicle into a polar orbit. The weight of that additional fuel would have required a rocket larger than the available Saturn 5 rocket.
(at around 26 mins) 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.
The mission patch shown at the beginning of the film is different to the patch the astronauts are wearing. The patch at the beginning of the film lists the mission commander first, command module pilot, and the lunar module pilot. This is correct. On the patch that the astronauts wear, the command module pilot and lunar module pilot's names are switched.
Some sound is heard in the moon scenes, despite taking place in a vacuum. For example, a sinister clicking when the space monsters are near, and a heavy thud when the rover is flipped. This could be a mixture of sounds conducted through the ground, nondiagetic audio added for the audience's benefit, and actual goofs. Which is which shall be left for the viewer to decide, and the longstanding debate on sound in space movies will not be continued here.
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. - The footage is presumably a raw copy of the transmissions between the Lunar Module and NASA. It is plausible that ground control would keep closer tabs on this special mission than the regular Apollo-missions.
(at around 11 mins) The film does not state that the far side of the Moon never receives sunlight. The astronauts are not on the far side of the Moon. The comment about areas that never receive sunlight was about areas at the bottom of deep craters where the ground is always in the shadow of the crater wall. This does occur in many areas near the Moon's polar regions, which is where this movie takes place.
When moving around on the moon, the astronauts do not appear to be affected by the lighter gravity. They walk normally, even shuffling their feet at times, except in the stock footage from actual astronauts. Even the footprints from the cosmonauts are evenly spaced, as if they had been walking in earth's gravity.
When the two astronauts are driving the Rover, trying to find back the Russian capsule, the skyline of a city can be seen in the background for a few seconds, revealing that the scene was shot on Earth, rather than the Moon.
At the beginning of the movie it is stated that in order to conceal the additional manned mission to the Moon, the DoD justifies the launch of the extra Saturn V rocket with the need of putting a very heavy payload in Earth's orbit. However, the launch footage of Apollo 18 shows liftoff of a complete Saturn V with escape tower. As the latter have been so far used only in crewed launches, this would have been revealing (at least in part) of the manned nature of the mission.