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: 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: 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: The ultimate goal was to orbit Jupiter to study the Monolith also in orbit around it.
Grumpy Scot