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)
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)
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.
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.
Time Crash - S3-E15
Continuity mistake: At the end of "Last of the Time Lords", the Doctor flicks two switches on the console just before the Titanic hits. In the same scene in "Time Crash", the last control he hits is a large button.
Audio problem: Near the beginning of the episode when we first see Bannakaffalata, he says "Christmas is funny", yet his lips don't match what he is saying. (00:01:45)
Continuity mistake: When the Doctor interrupts Mr. Copper's incredibly inaccurate description of Earth society to ask him where he got his information from, in a shot facing Mr. Copper, the Doctor's raised hand has only one finger extended. In the next shot, facing the Doctor, he has two fingers extended, with the other two only loosely curled. Shortly after this, the Doctor scratches his temple with that same hand, only for it to be absent in the next shot facing Mr. Copper. (00:11:40)
Continuity mistake: After Rickston asks the Doctor how "Mr. and Mrs. Fatso" (Morvin and Foon) are going to get through a narrow gap, when the Doctor responds that they're going to make the gap bigger, he passes Rickston a piece of metal. The steel bar's appearance changes between shots. (00:27:45)
Continuity mistake: When Mr. Copper is talking about how space-lane fraud could get him ten years in jail, the cut on his forehead changes sides, as does the panel behind him, revealing the shot to be flipped. (00:36:25)
Continuity mistake: After Morvin falls to his death in the engine, when Foon tearfully demands to the Doctor that he bring him back, and he tells her he can't, Foon's hand is gripping the railing in one shot with the two of them, but missing in a shot facing the Doctor as he says, "I know. I'm sorry." (00:37:45)
Continuity mistake: When Astrid tells Mr. Copper that she's going down to Deck 31 to find the Doctor, she's using her left hand to fit a teleport bracelet on her right wrist. In a shot facing Mr. Copper immediately after as he wishes her good luck, her left arm is suddenly by her side. (00:50:55)
Continuity mistake: The meteors are shown approaching and hitting the ship on the starboard (right) side. Twice, however, they are erroneously described as being to port (left): When the meteors are first seen on the scanner by Frame, and later when Frame tells the survivors in Kitchen 5 to go starboard because the port side of the ship is impassable.
Revealing mistake: Max Capricorn is a cyborg, with his head being the only remaining part of his original body, wired up to a mobile life support system. If you look closely during his scenes, whenever he turns his head, the costume the actor is wearing to hide his body becomes apparent, as the wires and cables below Capricorn's head also move slightly.
Chosen answer: The Master knows that deep down, he deserves death for the crimes that he's committed throughout his life, and since he regards The Doctor as his arch-foe, he expects it to be at his hands. The fact that The Doctor is still willing to forgive him for all of his crimes hurts him more deeply than death would.
Captain Defenestrator