Other mistake: After the hybrid Dalek Sec explains the Daleks' plan to harness the power of a solar flare to the Doctor, when the Doctor asks how many minutes until the flare arrives, Sec says it's in 11 minutes. A fair amount of action and backstabbing later, when the Doctor and Laszlo arrive at the top floor of the Empire State Building and after the Daleks take back control of the elevator, the Doctor says that the solar flare arrives in 6 minutes. It is a considerable stretch for everything that happens between those two moments to take place in only five minutes.
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)