Factual error: Corey is in solitary confinement on an asteroid. However, asteroids are neither large enough nor stable enough to hold an atmosphere. In addition, the distance from earth stated in the episode wouldn't be much further than the moon; there are no asteroids in a stable, regular orbit around the the moon or the earth, nor around the sun anywhere that close to earth.
Other mistake: The supply crew arrives at the asteroid every 3 months, as established by the dialogue between Corry and the astronauts who bring him the female robot. However, Corry's narration reveals that he has been living with the robot for 11 months when the next supply ship arrives.