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.
Suggested correction: The shuttle lands "on its back" with legs extending beyond the engines. As in most traditional sci-fi, and ALL actual, space flights to date, the launch (and landing) orientation for humans is to be on one's back. This minimizes blood being sucked down to your feet if you were sitting upright at launch - you could pass out. So we see this when the shuttle lands on the moon - the cockpit (red window) faces up (pilots on their backs, facing out the window). When we presume that the passenger cabin was 180 degrees spun around from the cockpit seating, they're still on their backs. Any loose objects would have been stowed before landing - the airlines don't lock down your bags, newspapers and coffee cups, right? They're loose in the cabin during flight, but put away on takeoff and landing.
Airliners do not fly upside down. The Orion shuttle cannot possibly operate the way it does if it lands in a gravity environment - some rooms are upside down relative to others - why else would the stewardess do the 180 degree vertical walk? It is an idiotic design flaw, and the posting is 100% correct.
The Aries passengers sit and stand with their feet down towards the moon. The pilots sit with their back down to the moon, as conventional astronauts do on Earth. But the attendant's 180-degree walk is completely wrong to the orientation of the shuttle's interior: it should have been only 90° if you look at the Aries exterior. One assumes that Kubrick preferred a longer, more cinematic shot, over a technically accurate shot. But nobody was upside-down to the moon.