Revealing mistake: When the Doctor calls Rose when she is with the Daleks, you can see on the screen of her phone that the call has been going on for at least 57 seconds, but she just answered the call. (00:06:50)
Audio problem: Mickey asks Rose why the Daleks are keeping them alive. When she responds, "They might need me," her mouth movements are not in sync with the words. (00:09:25)
Continuity mistake: After Pete tells the Doctor that Mickey went ahead because he wanted to find Rose, the Doctor asks him if he knows that Rose is his daughter from a parallel universe. The problem is that in Pete's last scene in "The Age of Steel", the Doctor saw Rose call Pete "Dad", leading to Pete departing in a hurry. (00:15:05)
Revealing mistake: In the Torchwood building, a large group of Cybermen start shooting at the Daleks and the Genesis Ark. The Daleks shoot several of them, and you can see a Cyberman that, thanks to hilarious CGI, just collapses like a sock without any physical regard that he is wearing tough metal leg armour, is floating a little off the ground, and falls way too fast than physical laws could allow. (00:25:15)
Continuity mistake: When Rose is hanging onto the lever and beginning to lose her grip, in close-ups of her face her body is facing the other wall of the room, perpendicular to the floor. In shots showing her and her hands on the lever, her body and head are facing the floor. (00:35:55)
Visible crew/equipment: When Rose runs and hugs her mother, near the end of the episode, at the back wheel of the jeep, you can see someone's foot going down and then back up. (00:44:50)
Revealing mistake: When the Doctor and Rose are talking at the bay, the Doctor's hair is blowing in the wind, but it's not when he is shown in the TARDIS. Considering the image of him on the beach is a projection of him in the TARDIS, the two versions should match. The actor was obviously on the beach recording his lines with Rose and back on a set doing the inside scenes.
Continuity mistake: When the two Cybermen meet the Dalek for the first time, they are exterminated. They fall directly in front of the Dalek, but when the camera angle changes to show the second Cyberman hitting the floor side on, you can see the Dalek in the background. The Cybermen both fell straight forward, so it shouldn't have been possible to see the Dalek when seeing the Cyberman side on in the next shot, as the Dalek is facing them both directly.
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)
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)
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)
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)
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)
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 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)
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: 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)
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.