Deliberate mistake: When Dave is in the pod arguing with Hal to let him back in, various patterns of light are projected on Dave's face presumably from the video screens that say NAV and COM and such. Light on such a screen would diffuse and not project like this. It is likely those screens had rear projection and they merely removed the screens for this effect.
Deliberate mistake: On the space station after Dr. Floyd has just gotten off the elevator and is talking to a receptionist, the moon image in the window is revolving with the exact appearance it had when Floyd was in the telephone booth when the camera angle is perpendicular to the window and presumably parallel to the station's rotational axis. In the receptionist scene, the view of the window is at an angle yet the rotating moon image is the same. This would require a different axis of rotation for the space staton - one in which the station would be wobbling.
Answer: As author Arthur C. Clarke explained it, the first Monolith (the one seen at the beginning of the film and then buried on the Moon) was a space probe from an incomprehensibly more advanced alien intelligence that resided inside a star elsewhere in the cosmos. The Monolith's objective was to seek out lifeforms that had potential and "tweak" their neural evolution, causing them to evolve toward intelligence. In the case of Mankind on Earth, once the modification was made, the Monolith probe retreated to the Moon and waited 4 million years for Mankind to reach it. When Mankind reached the Moon, the Monolith sent a signal to the next phase of the experiment, which was another Monolith in orbit of Jupiter. When Mankind reached the Jupiter Monolith in a matter of months, the Monolith acted as an interdimensional portal to the other side of the universe, transporting the evolved human specimen to its creator (that resided within a star). The creator intelligence found the specimen (Dave Bowman) to be of acceptable quality and rapidly evolved him to the next level, a Star Child. The Star Child is a "godly" evolution of Mankind. The Star Child chooses to instantaneously return to its home planet (Earth), where it stops a nuclear war.
Charles Austin Miller