Revealing mistake: When we see the space station from the cockpit of the approaching shuttle, the station does not appear to rotate because the shuttle is rotating at the same speed. OK...except that the station IS still rotating with respect to the sun, which means that the light source and shadows on the station should be moving.
Revealing mistake: Whenever Dr. Nemur is smoking, you can tell the cigarette's not lit, because you can't see any smoke. When Mrs. Kinnian smokes in the movie, plenty of smoke is visible.
Revealing mistake: Early in the opening scene, Barbara and her brother Johnny are going to put flowers on their father's grave. As the two of them approach the gravesite, with Barbara leading the way around a low cut bush (centre screen), the camera angle changes and suddenly their positions in their walk have unrealistically changed. After Barbara says, "There it is," the camera angle changes and we now see Johnny walking behind the bush in a spot he had already walked (so he walks a small patch of lawn twice). Barbara instantaneously changes from walking full stride with her hands in her coat pocket to a momentary standing position with legs apart and the beginning of an initial step. Her hands are now no longer in her pockets but swinging at her side.