Factual error: A reflection of a full Moon is shown near the end. When Earth is viewed from the Moon earlier, over half of it is illuminated by the Sun. For it to be full Moon, the entire Earth would have to be dark. In addition, the place where the hospital was transported to was dark, and not sunlit. (00:37:45)
Continuity mistake: Martha reaches her right hand up to open the window, prompting Julia to panic and say "Don't! We'll lose all the air!" When the shot changes as Martha points out that the windows aren't exactly airtight, her right hand is suddenly lowered. (00:09:47)
Continuity mistake: When Martha is walking up to the hospital just before the motorcycle gear-clad slab bumps into her, her right hand goes from by her side to holding her purse strap between shots. (00:02:15)
Continuity mistake: When the Doctor puts his tie back on after returning from the morning, the collar of his shirt is noticeably askew as a result. Just moments later, when Martha enters the TARDIS for the first time, the collar is neat again, without him having done anything. (00:41:00)
Continuity mistake: When Martha is talking to the Doctor, who is posing as a patient, about her encounter with him in the street earlier, which he doesn't remember, she takes her stethoscope off her neck. The camera cuts to the Doctor, then back to her, and she's taking it off again. (00:04:15)
Continuity mistake: When the Doctor is looking out the window while asking Martha if there's a balcony on the floor of the hospital they're on, in close-ups of him only his right hand is visible, resting on the sill between two windowpanes, and his left arm is by his side. In a wide shot from outside looking in, his left arm is stretched out with his left hand gripping the divider between two windowpanes, in a spot where it should have been visible in the preceding shot. (00:10:05)
Continuity mistake: When the Doctor and Martha open the doors to the balcony, in a shot facing them, Martha lets go of the handle of her door and it swings completely open. In the next shot, from behind, Martha is still holding the doorknob. (00:10:35)
Continuity mistake: When the Doctor is telling Martha that he was just wandering and not looking for trouble, in the wide shot, he's rubbing his chin. In the close-up immediately afterward, his hand has jumped to his hair. (00:19:45)
Visible crew/equipment: When the Doctor is being held by the slab in the MRI room, there are some shots where what appears to be a lighting screen is reflected in its helmet. (00:29:55)
Continuity mistake: When Martha and the Doctor are talking in the alley at the end, he's leaning on the TARDIS. His exact position keeps changing between shots. (00:39:10)
Audio problem: When Martha says "We're on the Moon. We're on the bloody Moon," her reflection is visible in the window in front of her. Her lips don't move. (00:07:35)
Visible crew/equipment: As the black suited figure stops to look at Martha, the crew and equipment are reflected in the helmet and visor. (00:02:30)
Factual error: When the Royal Hope Hospital is transported to the Moon, the area it is in is dark, indicating they are on the side of the Moon not currently facing the Sun. However, in a wide shot of the hospital on the Moon, something that looks like the Sun is visible, something that the illumination of the landscape and the Earth shows cannot be visible. (00:07:40)
Suggested correction: When the reflection of the full Moon is viewed it is night time several hours after we saw the Earth from the Moon.
Peter Wallace
Yeah, no, the phases of the Moon don't work like that. New Moon and Full Moon are two weeks apart. Since the Moon appears to be, judging by the appearance of the Earth, between New and either First or Last Quarter, it is impossible for a Full Moon to be visible later that night.