
Visible crew/equipment: When the astronauts are approaching the monolith on the moon, you can see the reflection of the cameraman in the visor of the first astronaut off the ramp, in the close up of him walking around the monolith. This shot was personally filmed by Stanley Kubrick and the reflection is his own. (00:48:40)

Visible crew/equipment: When David walks with the case in the hand inside the Discovery One, you can see the dolly track below at David's feet blending in the structure. (01:12:12)
Visible crew/equipment: During one of the scenes where an astronaut does an EVA (Extra Vehicular Activity or "Space Walk"), you see him floating slowly from the Pod shuttle towards the Discovery. This was filmed by hanging the pod on the ceiling and lowering the actor from it with a rope towards the camera that's pointing upward. If you look carefully, you can see the shadow of the rope.
Visible crew/equipment: In both EVA scenes, first when Dave retrieves the AE-35 Unit, and when Frank goes to re-install it, there are shots of Discovery in the background, the pod in the foreground and the astronaut floating between. And in both of these shots, the pod rotates 180 degrees. In the front window of the pod, we can see reflected images of the film set and equipment as the pod rotates.
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