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.
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: 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)
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.
Continuity mistake: When Donna starts fiddling with the Adipose necklace she stole, this causes an Adipose to be created out of Stacey's fat cells. When this begins, Stacey is in the upstairs bathroom applying lip gloss, and she's holding the applicator wand when her stomach begins to move. When she pulls up her shirt to look at her distending stomach in the mirror, the lip gloss wand is gone. (00:07:15)
Other mistake: The security guards shoot away the lock on the door, which they then kick down with no real effort. But the door would still be held in place by the hinges - they don't kick it with enough force to rip the hinges out, and even if they had, we can see that there's no damage on the hinge side of the door anyway to demonstrate their forcible removal. (00:24:20)
Other mistake: When the Doctor and Donna get onto the roof, after he sonics the door shut behind them, as they run for the crane for the window washing cart he puts his sonic screwdriver in his mouth, holding it between his teeth, and pulls something out of his pocket. It looks like he might be carrying Miss Foster's sonic pen - except that at this point in the episode, it hasn't yet been revealed. (00:24:20)
Revealing mistake: When the Doctor and Donna are attempting to smash open a window while stuck in the window-washing cart, there is a shot of them from above just before Foster cuts the cable in which banging sounds are heard and the cart is shaking, but if you look closely at them they aren't actually touching the window at all. (00:26:10)