The Christmas Invasion - S2-E2
Continuity mistake: When Daniel Llewellyn meets Harriet Jones, she pulls out her ID card when she introduces herself. The scene cuts to a shot of Llewellyn saying that he knows who she is, and when it cuts back to Harriet, the ID card has vanished without her making any movement to put it away. (00:16:10)
The Christmas Invasion - S2-E2
Continuity mistake: When Rose goes to look at the Doctor in bed while Harriet is speaking on TV, the bedding has changed from when it was previously seen. (00:28:05)
The Christmas Invasion - S2-E2
Continuity mistake: After the Sycorax ship has arrived above London, when Rose has decided that they need to shelter in the TARDIS and is explaining this while preparing to put a housecoat/dressing gown/bathrobe on the unconscious Doctor, the garment jumps between the bed and her hands in a few shots. (00:30:25)
The Christmas Invasion - S2-E2
Factual error: The episode kicks off with a reuse of the zoom-in from orbit first seen in "Rose." As the sunny North Pole indicates, the Earth is depicted as if it is the height of Northern Hemisphere summer, even though as the title of the episode indicates, it begins on Christmas Eve, three days after the northern Winter Solstice when the Pole is in darkness. (00:00:05)
Continuity mistake: When Rose gets into one of the hospital's elevators early in the episode, stock footage of an elevator descending is shown. When the Doctor, Rose and Cassandra (possessing her) go into an elevator shaft later on, it looks and is shaped completely differently. (00:34:05)
The Christmas Invasion - S2-E2
Revealing mistake: When Daniel Llewellyn is looking up U.N.I.T. staff records on the computer, at one point a control panel for a DVD playing program is visible onscreen, showing that the special U.N.I.T. user interface is a video. (00:26:25)
Audio problem: When the Doctor confronts Mr. Finch/Brother Lassar in the school pool, there is a wide shot of the Doctor from across the pool as he asks Finch, "Who are you?" His mouth isn't moving. (00:23:10)
Continuity mistake: When the Sphere Chamber is first shown, there is a rolling staircase set up just below the Sphere. Rajesh Singh is shown climbing the staircase and nearly touching the Sphere. However, when the room is next seen, when Raj hears that the Doctor is coming and walks up to look at the Sphere again, the staircase has vanished. Later, when the Doctor and Jackie are shown into the room while Yvonne gives them the Torchwood tour, the staircase is still missing, and it's more obvious that it is no longer in the room. It does not reappear for the remainder of the two-parter.
Rise of the Cybermen (1) - S2-E8
Continuity mistake: In this episode's TARDIS scenes, the yellow padded seat is positioned so that it's on the side of the console closer to the door, so people sitting on it are facing away from the door. In all other episodes featuring this version of the console room, the seat is positioned on the side of the console opposite the door.
The Christmas Invasion - S2-E2
Continuity mistake: When the robotic Christmas tree attacks Rose, Jackie and Mickey in the Tylers' flat, it barrels through the internal window and destroys a supporting pillar separating the living room from the main hallway. Later in the episode, the pillar is seen intact. (00:13:30)
Continuity mistake: In the sphere room the Doctor briefs Yvonne and Rajesh on the void. As he sits down in front of them you see Jackie's feet start walking towards them but the next cut behind Yvonne and Rajesh facing the Doctor shows Jackie isn't there. (00:25:15)
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 Chip/Cassandra finishes the line about being a walking doodle, he's smiling. After the cut, he's straight faced.
Continuity mistake: When the Doctor and Mrs. Moore are walking through the tunnel of Cybermen, there is constantly a light source in front of them. When the shot looks ahead, there are no lights. This is due to the cameraman giving more light so this all can be filmed.
The Impossible Planet (1) - S2-E11
Continuity mistake: When Rose, the Doctor, and the others are running across the walkway a stream of steam appears and disappears between shots. (00:03:55)
Visible crew/equipment: When Rose and the Doctor are riding after landing, you see the camera, crew and lighting equipment reflected in their glasses. (00:04:00)
Chosen answer: No, no information is avalible for the identity of the entity.
Repo_Man