Continuity mistake: In the episode "New Earth", the Doctor said that the titular planet is in the galaxy M87. Upon returning to New Earth in this episode, he says that the planet is 50,000 light-years from where the original Earth used to be. That's a difference of over 50 million light-years, since M87 is a very real galaxy in the centre of the Virgo Cluster, that far away from the Milky Way. (00:02:55)
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)
The Impossible Astronaut - S6-E2
Continuity mistake: When the school bus pulls up to drop Amy and Rory off in Monument Valley, there are no other vehicles in the area. When the bus pulls away, the Doctor has suddenly appeared with a vintage station wagon, parked by the side of the road where it should have been perfectly visible. And he was sitting on the hood, implying he'd been waiting there for a bit. (00:02:45)
The Impossible Astronaut - S6-E2
Continuity mistake: When the Doctor starts walking over to the lakeshore after the astronaut appears, he's still holding the wine bottle in his right hand. In the next shot where we can see his hand, the bottle is gone, without him having stopped to put it down. (00:06:34)
Continuity mistake: When River is talking to the Roman commander after disintegrating a piece of furniture with her pistol, she is shown raising her fingers from the pistol's grip in a shot facing the commander. However, in all following shots facing her, her fingers are still lowered. (00:17:50)
The Lodger - S5-E11
Continuity mistake: When the Doctor is flipping through a book while talking with Amy on his earpiece, in the close-up shot he's using his right hand, but in the wide shot is using his left hand, going through the pages the other way. (00:12:10)
Continuity mistake: Near the end, when the Doctor is explaining to Amy that she will forget Rory when the crack in time is finished eating him because he's part of her personal timeline, and he has his hands on her temples, Amy's hair is covering her ears in some shots, but not others. (00:40:56)
Continuity mistake: When Ambrose, while standing with Elliott, admits to killing Alaya, in the first shot, Elliott is standing in front and to the right of Ambrose. In the second shot, he's standing to her left. (00:27:52)
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)
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.