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)
Other mistake: The stet radiation in the red room is able to disintegrate living beings, with the exception of the immortal Jack. People not going in the room are shown to stay out of the line of the door when it's being opened, lest they be disintegrated. When Jack comes out of the room after having finished in there, the Doctor, telephoning the rocket, is in line with the open door yet remains completely fine. (00:35:15)
Other mistake: When Professor Yana shows Martha his pocket watch, which she comes to realise is a Chameleon Arch, she initially finds it familiar from the appearance of the back, and eventually asks him if she can see the front. Before she eventually sees the front of the watch, there is a shot where the front is hidden to the camera, but should be perfectly visible to Martha, just as Yana says "It's old. It's not meant to be." (00:34:40)
Continuity mistake: When Sally Sparrow is about to take the key from the weeping angel, at first the key is on a piece of string, and that string is wrapped around the weeping angel's left hand. In the next shot, and when she pulls the key out, the string is now only in the angel's palm. (00:10:30 - 00:11:10)Riversong57
Doctor: So, that's the trap. Or the test or the final judgment, I don't know. But if I kill you, I kill her. Except that implies, in this big grand scheme of Gods and Devils, that she's just a victim. But I've seen a lot of this universe. I've seen fake gods and bad gods and demi-gods and would-be gods - out of all that - out of that whole pantheon - if I believe in one thing... Just one thing... I believe in her.