Revealing mistake: When the astronauts are on the way to the monolith on the Moon, there are two windows seen within the interior of the small space shuttle. During their small lunch, in the left window, the horizon is seen as the surface of the Moon is flowing back against the direction of the flight. However, although sometimes this horizon fills up to half of the window, no horizon can be seen in the right window despite being located directly beside the left window. Nevertheless, the inclination of the Lunar surface should allow for it to be seen.
Revealing mistake: During the "Dawn of Man" sequence, the ape-man scenes were shot on an indoor stage with projected background images on a huge screen behind the stage. The screen itself was a highly reflective cloth. In most shots, it is quite convincing, but in several (especially when facing the aggressive, victorious group during the first fight, then again when facing the tool-using group in the last fight), the rear screen appears to be a patchwork of smaller pieces of cloth as very obvious puzzle-like shapes of varying reflectivity appear in the sky. Once you notice them, it's incredibly distracting. It was originally parallel strips, but they were VERY visible as vertical lines so they were torn into a patchwork to make lines less obvious.
Revealing mistake: When Dave Bowman is attempting to break into the Discovery after being locked out by Hal you can see, reflected in the Pod window as the Pod is spinning around, the edges and top corner of the small set of the Discovery hatch area. (Second timecode is accurate for DVD release)
Revealing mistake: In the sequence of the shuttle approaching the moon the pilot talks to Dr. Floyd. Floyds food-tray moves away from his knees because of the zero gravity in the shuttle. But it doesn't drift straight away, it swings like a pendulum showing that the tray is hanging on a string.