Continuity mistake: When Joseph Green (really Jacrassa Fel-Fotch Passameer-Day Slitheen) picks up the skin of Oliver Charles from the Cabinet table, he picks it up with his left hand in the first shot but is holding it with his right hand in the next. (00:32:30)
Continuity mistake: When Harriet Jones is hiding in the closet and spying on the Slitheen attacking General Asquith, wide shots of the closet door have it in shadow, but close-ups of Harriet have the part of her face that is visible illuminated.
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)
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)
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)
Revealing mistake: At the end of the episode there is a side shot of the Doctor leaving the TARDIS in which you can see inside, but the control room isn't visible, just the side of the police box, with light from outside shining through the window. (00:38:00)
Continuity mistake: During the opening montage, showing the Slitheen incapacitated by electrocution, when Margaret drops Indra's body and stumbles back, a close-up of the body on the floor shows her legs without the pulsing electricity covering her entire body, which is visible in other shots.
Continuity mistake: When Rose and Adam are in his workshop talking about aliens, during the exchange where she asks him about people who claim they've been in spaceships and he responds that he thinks they're nutters, Rose is poking around with her right hand at a storage shelf on the wall before moving her hand to a pile of boxes stacked on a table. When the scene cuts to a close-up of her, her hand has jumped back to the shelf. (00:12:40)
Revealing mistake: When they show the soldiers killed by the Dalek, in both the hallway outside the cage and the large room in weapons testing, they show some casings which were ejected from the soldiers' guns. The casings still have projectiles in them. If used, they would have been in magazines and would never fall out like they are shown.
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"
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: 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 Suki discovers the bodies on Floor 500, she drops her flashlight, but in the next shot she's holding it again. (00:15:20)
Continuity mistake: When the Doctor is restrained by two of the Editor's corpse minions, and the Editor demands to know who he is, the hand of the one holding the Doctor's right arm moves between his chest and shoulder several times. (00:30:50)
Revealing mistake: When the Editor activates the Doctor and Rose's manacles, the right manacle binding Rose's wrist snaps open as they are shocked. (00:35:12)
Father's Day - S1-E8
Continuity mistake: When Rose checks her messages while riding in Pete's car and hears the very first phone call instead, the positions of her fingers change between the wider shot and the close-up. (00:13:30)
Father's Day - S1-E8
Plot hole: In "Aliens of London", it is established on a 'missing person' poster that Rose Tyler is approximately 19 years of age in March 2005 (The poster says 'missing since 6 March 2005'). This means that she must have been born prior to March 1986. However, in "Father's Day", which is dated 7 November 1987, Rose is still a baby in her mother's arms, when she should be a toddler aged approx two.
Continuity mistake: When the Doctor takes to the nightclub stage to ask if anything has fallen from the sky, he has his right hand and arm up and gesticulating. But in several other shots of him from behind, it is his left arm that is up and moving. (00:04:20)
Continuity mistake: When the Doctor meets Nancy, when she warns him not to answer the TARDIS' ringing (fake) door phone, in a shot facing her he's holding his jacket away from his chest, but in the next shot facing him that hand is empty. (00:06:55)
Plot hole: Nancy seems to have the unique ability to whistle with her fingers in her mouth - even though she's wearing gloves. (00:10:55)