Continuity mistake: When the Doctor and Martha open the doors to the balcony, in a shot facing them, Martha lets go of the handle of her door and it swings completely open. In the next shot, from behind, Martha is still holding the doorknob. (00:10:35)
Continuity mistake: When the Doctor is telling Martha that he was just wandering and not looking for trouble, in the wide shot, he's rubbing his chin. In the close-up immediately afterward, his hand has jumped to his hair. (00:19:45)
Visible crew/equipment: When the Doctor is being held by the slab in the MRI room, there are some shots where what appears to be a lighting screen is reflected in its helmet. (00:29:55)
Continuity mistake: When Martha and the Doctor are talking in the alley at the end, he's leaning on the TARDIS. His exact position keeps changing between shots. (00:39:10)
Continuity mistake: When the Doctor picks up a mug and a pencil to use as props to explain to Donna how she was pulled into the TARDIS, he is initially holding the pencil by the blunt end. The scene cuts to a shot of his face, and suddenly he's holding it by the sharpened end. (00:28:35)
Factual error: During the rooftop scene, Donna checks her watch and says that it's half past three, or 3:30 PM. In London on December 24, that's roughly 45 minutes before sunset. However, not only is the angle of sunlight during this scene much higher than it should be for the date and time, the Sun proceeds to remain up for some time longer, including during the wedding reception and when the Doctor discovers the tunnel underneath H.C. Clements leads to below the Thames Barrier, even though it really ought to have set by then.
Continuity mistake: When the Doctor is giving the Racnoss Empress an ultimatum, the position of his hands on the railing in front of him changes between shots. (00:48:00)
Factual error: During the chase on the motorway, many deciduous trees sporting lush green leaves can be seen in the background, in sharp defiance of the fact that it's supposed to be Christmas Eve and their branches should be bare. In addition, despite having chosen to wear a sleeveless wedding dress, Donna is remarkably unbothered by the fact that it should be fairly brisk outside, probably somewhere around freezing.
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)
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.
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 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)
Factual error: The opening shot of the episode reuses the zoom-in from orbit originally used in "Rose." The North Pole is sunlit, as it would be at the height of summer. "The Runaway Bride" takes place on Christmas Eve, four days after the Northern Hemisphere's Winter Solstice, when the Pole would be facing away from the Sun, in darkness. In fact, this was the second Christmas special in a row to make this mistake, after "The Christmas Invasion." (00:00:05)
Audio problem: When Martha says "We're on the Moon. We're on the bloody Moon," her reflection is visible in the window in front of her. Her lips don't move. (00:07:35)
Visible crew/equipment: As the black suited figure stops to look at Martha, the crew and equipment are reflected in the helmet and visor. (00:02:30)
Revealing mistake: At the end when the Doctor makes it snow, in the wide shot you can see the snow blows in from the left side, showing that they used a snow machine just off-camera. (00:54:30)
Revealing mistake: When the Doctor goes to toss the trio of Christmas balls up, the two times after the first toss are re-used shots of the first toss. His movements of his right arm to bring up the controller are too exact to be coincidence. (00:50:15)
Visible crew/equipment: As the Doctor tries to get Donna to jump to the TARDIS, as the camera is in a close up on her in the taxi, the yellow camera vehicle is reflected on the cab's paint. (00:12:50)
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.