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: 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.
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 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: 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)
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)
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)
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)
