Continuity mistake: When the Doctor is standing in front of the giant whirring fanblades, just before he passes the first one, which side of his jacket is blowing away from his body changes between the wide shot and the close-up. (00:35:20)
Continuity mistake: After the Doctor freezes the Auton arm, its index and middle fingers are curled, while its ring and pinky fingers are straightened. When the Doctor and Rose are in the stairwell, most noticeable when they emerge at the bottom, the fingers of the arm are now all slightly curled.
Continuity mistake: Partway through the episode, there's a wide shot of London, with an undamaged Big Ben visible. The inciting incident of the previous episode was a spaceship crashing into the clock tower, severely damaging it. (00:25:40)
Visible crew/equipment: After the acting Prime Minister gives orders to the sergeant and the lift doors close, the soldier turns around. As he issues orders, the boom mic is reflected on his goggles. (00:05:25)
Continuity mistake: After the Doctor gives Rose instructions, he crosses his arms and leans against the TARDIS. In the close up, he does it again. (00:00:25)
Continuity mistake: The Doctor pulls the arm off Rose, deactivates it, and the fourth and fifth fingers are the last to stop moving. When the angle changes, the first two fingers are the last to stop.
Continuity mistake: When Suki goes to leave the lift on floor 500, her arms are by her sides, then suddenly both hands are gripping the strap on her bag. (00:14:00)
Continuity mistake: When Rose is telling Auton Mickey that she thinks they should stay away from the Doctor because he's dangerous, a lock of her hair in front of her face tucks itself behind her ear when the shot changes to a close-up. (00:24:42)
Factual error: The upper peninsula of Michigan is missing on the map of the US shown on Van Statten's monitor.
Suggested correction: In that era of Doctor Who the Earth was being invaded by aliens on a regular basis. Since the story is set in the 'future' year of 2012, anything may have happened to wipe that part of Michigan off the map.
I'm from Michigan and when I noticed the UP missing, I jokingly said to a friend "looks like Canada stole that finally"
Character mistake: The Doctor comments that the destruction of Earth will cost 5 billion lives. At the time of the episode (2006, one year on from when Rose met the Doctor), the population of Earth was around 6.5 billion. (00:25:10)
Audio problem: When Rose is sitting in the observation deck, after she looks at the tree cutting and suggests they might be related, when she puts it back down, it makes a "clink" sound, as if made of metal, despite being in a sort of cardboard cup. (00:15:20)
Continuity mistake: During Mickey's struggle with the plastic trash bin, the angles of sunlight and shadows keep changing between shots. (00:22:20 - 00:23:20)
Revealing mistake: When the Doctor fires a champagne cork into Auton-Mickey's head, the lack of spraying or leaking wine, even when the Doctor is seen holding the open bottle horizontally immediately afterwards, makes it quite clear that the champagne bottle is actually empty. (00:25:23)
Continuity mistake: The Auton in the red shirt is seen starting to come down the escalator, then at a quarter of the way down, then at the top again, just starting down. (00:38:22)
Revealing mistake: In the underground scene in the Nestene lair, the CGI used to create the Nestene is horrendous. And in a shot from behind the Doctor, the Nestene looks like a whole bunch of orange pixels.
