Continuity mistake: In the last scene, when Amy attempts to seduce the Doctor, she pulls his suspenders off his shoulders and he pulls them back on. As a result, the suspenders change position between shots.
Continuity mistake: In the scene at the beginning with the boy on the Vator being sent "below", the Smiler in the lift is shown with its head turned to its frowning face shortly before it is shown changing its expression. (00:02:23)
Continuity mistake: When the Doctor first meets Liz 10, during their conversation, her hood is pulled completely over her hair in shots facing her, but some of her hair is sticking past her hood in shots facing the Doctor.
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 End of Time: Part Two - S4-E18
Audio problem: During the climax, when the Doctor has Wilf's old service revolver and is alternately pointing it at the Master and Rassilon, there's a cocking sound every time he turns. Not only is the handgun a revolver, so it only needs to be cocked once, the Doctor is only shown actually cocking the gun once, when he first points it at Rassilon. (00:44:10 - 00:45:55)
Continuity mistake: The episode repeats the closing scene of "Doomsday", when Donna unexpectedly appears in the TARDIS. However, several details are different. One, the console room is more brightly lit than in the previous episode. Two, the shirt belonging to Rose that Donna finds draped over a railing was not present. Three, the Doctor's coat (draped over a ceiling support) has shifted in place, despite not being touched. (00:01:15)
The Sound of Drums (2) - S3-E12
Continuity mistake: On the Valiant's bridge, when the Doctor is telling Martha and Jack about his plan to slip one of the perception filter keys around the Master's neck while holding his key, the position of the key changes in his hand, from being held by the wide end to being held by the narrow end. (00:37:15)
Deliberate mistake: The Globe Theatre is shown staging performances at night. In actuality, they performed during the day, when there was enough light, since this was pre-electricity. This was done both to make the climax of the episode scarier and because they shot on location in the real Globe, which still shows its plays during the day, and thus they didn't have a lot of time to shoot during the day there.
The Curse of the Black Spot - S6-E4
Continuity mistake: The pirate that Toby cuts on the hand with a sword in order to make him stay in the magazine is gone when the Doctor and Captain Avery return, but reappears on the spaceship at the end with the rest of the crew.
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)
Factual error: When the TARDIS is flying over London at the beginning, the London Eye is visible. It's supposed to be 1996, and the Eye was built later than that, for the new millennium celebrations. (00:00:30)
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: Just before Penny Carter tells the Doctor and Donna that she's going to report them for "madness", the Doctor is seen holding Miss Foster's sonic pen, which he threw in the trash just moments earlier. (00:42:10)
Continuity mistake: The registration of Milo and Cheen's car is shown on the computer screen and stated aloud as "4-6-5-◊-6." However, there is a shot of Martha and Cheen looking out the window where the car's registration sticker is visible, showing a different registration: "9-9-6-γ-1." (00:13:15)
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.
The End of Time: Part Two - S4-E18
Other mistake: Shortly after everyone arrives on the Vinvocci ship, when the Vinvocci and the Doctor run through the door on their way to the flight deck, the Doctor comes back to get Wilf, who didn't initially follow because he was mesmerized by the sight of the Earth from orbit. It's obvious that David Tennant went just behind the door and paused briefly before coming back into the room, which is not what the Doctor is supposed to be doing. (00:16:00)
Continuity mistake: During the scene on the hospital roof, when the Doctor is telling off the Atraxi while simultaneously choosing a tie out of several he stole from the locker room, the number of ties draped around his shoulders and the position of his hands changes between shots. (00:52:35)
Continuity mistake: When the Doctor sonics the payphone so Donna can call her mother, he's doing it with his right arm, then it cuts to close-up and he's using his left arm. (00:09:00)
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.
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)
Chosen answer: 1) When Stephen Moffat took over he ignored a lot of what had been developed before (there is not in-universe answer). 2) It would have killed Rose, so the Doctor absorbed the energy. His body regenerated before the energy could do a significant amount of damage that would prevent regeneration.