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.
Continuity mistake: In several scenes, we are given HAL's visual perspective as if seeing through his lens. This is done with an overlayed image of the lens on whatever area is in sight of the lens. As Dave is entering HAL's memory circuit room (red lighting), one shot again suggests we are again seeing what HAL sees, but there is no HAL lens located and oriented to provide the angle we see. A lens would need to be mounted on the narrow wall directly opposite the circular doorway, yet HAL's lens in this room is mounted on the 'ceiling'. (01:51:25)
Continuity mistake: In a sequence in the cockpit of the space ship approaching docking, the shot shows the two pilots and 3 monitor screens between them. The right-hand screen changes from a data display to a blank showing only the letters "GDE" (possibly "GOE"). The next shot is a close-up of the three monitors, and the right-hand one now shows its earlier data display. The other two do not show this behaviour. (00:25:00)
Continuity mistake: During Heywood's meeting with Elena and Dr Smyslov, he is introduced to their colleagues, including Dr Kalinan who is the women in the olive dress/suit. When they shake hands her coat is folded neatly over her seat, but before she sits down again with the camera now facing Heywood, the coat disappears. In an earlier shot prior to the introduction, the majority of Kalinan's coat is off the seat and when she stood the first time it probably fell, suggesting the handshake sequence was re-filmed after the actual meeting. (00:28:45)