Continuity mistake: The first time the two crew men in the moon buggy are seen, the numbers on their suits are eight and three. The next moon buggy scene, the two in the suits are numbered eight and three again at first, but when they're testing the domes, the numbers change to nine and zero.
Continuity mistake: As the experiment recreation progresses, and Helena identifies the spirit, the spirit appears with damage on the left side of its face, and a yellow sleeve on its right arm. When the camera is close up to the spirit, the damage and yellow sleeve change sides.
Other mistake: In the beginning, the Eagle was moving away from the alien planet, and as such, should have crash landed facing away from the planet. However, it was facing the direction it came from. If it traveled a fairly straight line, (and the trajectory suggests it did) then it should have crashed with the rear end facing the planet.