Continuity: After Dave Bowman takes his food out of the food slot, two of the containers in his tray exchange positions by themselves. When he first removes the tray, there is a dark red container all the way to the left and a grayish one next to it. When Dave makes his way to the table to eat, the red one and the gray one have switched places.
Factual errors: The earth is more colorful from space than indicated.
Continuity: In the lunar transport en route to Tycho, the photo that Floyd is looking at changes suddenly from color to black and white.