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)
Continuity mistake: In the scene when Donna asks the woman if she could borrow £10 because it's Christmas, you can see that Donna is wearing sports shoes instead of her usual white wedding shoes. (00:10:05)
Suggested correction: No, she's wearing the same shoes if you pay attention.
Never mind - she is wearing running shoes for no apparent reason.
Continuity mistake: The cab Donna's in passes a red vehicle on the bridge. A second later, it's nowhere to be seen looking back. (00:12:15)
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)
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)
Character mistake: When the Doctor is taking Donna to 4.6 billion BC to watch the formation of the Earth, he says that it is the furthest back the TARDIS has ever been. But in the 5th Doctor episode "Castrovalva", the TARDIS drifted to 13.2 billion BC and the formation of the galaxy. (00:40:35)
Continuity mistake: When the TARDIS arrives back from the formation of the Earth, the Doctor and Donna rush out leaving the TARDIS door open. And yet in the very next shot, the door is closed. (00:44:30)
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)
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.