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.