Corrected entry: As Sam is saying "Two weeks." and drawing smiley faces on the metal quarters, we see remnants of another take - previously drawn smiley faces that have since been erased (but not fully!). (00:34:45)
Corrected entry: In the scenes where the vehicle is rolling on the moon surface, you can see the dust trail behind the vehicle's wheels. However, on the moon, in the absence of atmosphere, the dust should actually fall straight on the ground, immediately. This computer generated effect was added to make it look real, but it makes it physically inaccurate.
Correction: The gravity on the moon is 1/6th of that on earth so objects (including dust) fall back to the furface of the moon slower than on earth. The fact that there is no atmosphere would not make ojects fall instantly back down. Check out Nasa video of real moon rovers in action. http://www.youtube.com/watch?v=0_YhYBxjpQU.
Particle don't fall back slower, but with a constant g/6 acceleration pointing down, which doesn't appear in the movie. In fact, the total time spent in a parabola that extends L=2m above ground due to an acceleration g is 2 times square root of 2L/g, which is 3.3s in moon's gravity. So the dust trail should disappear completely at the spot the rover was 3.3s before.
Corrected entry: In the outdoor scenes, why are stars visible? Even the real NASA moon missions said the stars would not be visible from the moon.
Correction: Direct quote from NASA website: "On the moon, the sky is black - even during the day - and the stars are always visible."
Corrected entry: What is the probability that both would happen: a. Harvest machine was ruined by first Sam. b. New Sam somehow arises from bed before it was meant/programmed to - accidentally eavesdropping on the same debate, which directly triggers his suspicion and indirectly forms the base for the whole movie. (I assume that the preceding Sam clones didn't destroy harvest machines, because if they did, there is no reason for central sending the "Aliza" rescue team.)
Correction: Films often rely on relatively implausible events to kick-start their narrative. These are not generally considered to be mistakes, except in very specific circumstances, which your question doesn't match.
Corrected entry: Gravity on the moon is only a fraction of that on earth. The filmmakers properly try to display this on those shots taken outside the station, on the surface of the moon. These shots are similar to what we are used to seeing on real historic moon walks. However, no effort at all was made to simulate the lack of gravity on those shots taken inside the station, resulting in a very unrealistic presentation of a moon settlement.
Corrected entry: How does the second Sam know where the first Sam has his accident and is stuck. He is a clone and just woke up knowing nothing but the stuff he is programmed to know, yet he is very devoted to find the first Sam.
Correction: GERTY had to tell Sam about the accident, make the new Sam think it was him in it, to explain the absence of the rover. When GERTY refused to let the new Sam go out to retrieve the rover, or even perform any of his duties outside the base, he grew suspicious that something was going on. He was only going out to investigate the rover; he had no idea he'd find and rescue his predecessor.
Corrected entry: The robot Gerty that appears throughout the movie has a small shelf on its right hand side (viewers left hand side, robots right hand side) on this shelf sits a dirty coffee cup but all through the movie the cup disappears and reappears several times.
Correction: The film takes place over a long period of time. It's reasonable to assume that the various Sams have taken coffees, or that Gerty tries to keep a fresh cup there, should Sam ever want one, but various tasks interrupt that.
Corrected entry: When the "first" Sam gets his hand burned by the hot water, he gets a burn because he sees a girl dressed in yellow with long dark hair sitting on his chair. We don't get an explanation as to who she was (not his wife or daughter because they are blond, and he doesn't know her as a 15-year-old).
Correction: Not being given an explanation for something is not a plot hole, which is best defined as something happening that benefits the plot while making no sense within the context of the film and established characters. Sam is hallucinating; the identity of the person that he's seeing is largely irrelevant to the plot and to provide a detailed explanation would simply have taken up valuable screen time and just sounded like an unnecessary exposition dump, disrupting the flow of the movie.
Correction: The director has stated in interviews that the hallucinated girl is Sam's daughter at her current age (14-15). He sees this through a sort of clone/twin telepathy.
Correction: Or was it an incomplete cleaning job after the last Sam clone?
Grumpy Scot