Factual error: The Koh-i-Noor, as depicted in this episode, looks absolutely nothing like the real diamond. The episode's gemstone is about the size of the palm of the Doctor's hand, and shaped in a stereotypical conical cut. The real Koh-i-Noor is much smaller and oval-shaped.
Continuity mistake: When the TARDIS crashes through the ceiling and lands in the tunnel, the side visible to the camera is not the one with the door. The camera cuts away, and when it returns to the TARDIS, on the same angle as before, the door is now facing the camera, as revealed by the sign and St. John's Ambulance medallion.
Continuity mistake: In the penultimate scene, just before the Doctor melts Amy's Flesh avatar, he points his sonic screwdriver, snapping it to its full length and opening up the four metal bits around the light at the tip. In the next shot, the screwdriver is "closed", but in the shot after that it's "open" again.
Continuity mistake: The Flesh, the substance that the gangers are made of, is capable of replicating people and their clothing. However, devices such as the sonic screwdriver are off-limits, which is why there is only one even after the Doctor's ganger is created. This is made clear when the Doctor tosses the screwdriver to his ganger before the ganger Doctor sets off to look for Rory. However, when the Doctor, Amy and the three human factory workers are trapped in the crypt with the overheating acid pool, the Doctor is seen using the screwdriver to scan the acid, even though the device should still be in the possession of the other Doctor.
Continuity mistake: When Idris/the TARDIS stumbles in the junkyard and the Doctor catches her, just before she tells him that one of her kidneys has failed, her right hand, holding a piece of circuitry, moves between in front of his chest in shots facing him and resting on his shoulder in shots facing her.
Continuity mistake: After the Sycorax ship has arrived above London, when Rose has decided that they need to shelter in the TARDIS and is explaining this while preparing to put a housecoat/dressing gown/bathrobe on the unconscious Doctor, the garment jumps between the bed and her hands in a few shots. (00:30:25)
Continuity mistake: The house that Donna and her family are shown living in in Series 4 is different from the house the Doctor dropped her off at at the end of her first appearance, "The Runaway Bride." You would assume they'd merely moved - except that in this episode, Donna and her family are shown living in their Series 4 house before the events of "The Runaway Bride", on the day Donna gets the job that leads to her meeting the Doctor in the first place.
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)
Factual error: The episode kicks off with a reuse of the zoom-in from orbit first seen in "Rose." As the sunny North Pole indicates, the Earth is depicted as if it is the height of Northern Hemisphere summer, even though as the title of the episode indicates, it begins on Christmas Eve, three days after the northern Winter Solstice when the Pole is in darkness. (00:00:05)
Continuity mistake: When the school bus pulls up to drop Amy and Rory off in Monument Valley, there are no other vehicles in the area. When the bus pulls away, the Doctor has suddenly appeared with a vintage station wagon, parked by the side of the road where it should have been perfectly visible. And he was sitting on the hood, implying he'd been waiting there for a bit.
Continuity mistake: When River is talking to the Roman commander after disintegrating a piece of furniture with her pistol, she is shown raising her fingers from the pistol's grip in a shot facing the commander. However, in all following shots facing her, her fingers are still lowered.
Continuity mistake: When the Doctor pulls the arm off the Auton and tosses it to Rose, the arm is bent at the elbow and solid plastic, with a smooth, clean break. Later, particularly noticeable when Rose has left the department store, the arm is hollow, with an unbent elbow and a jagged break. The arm continues to change between the two appearances for the rest of its screentime.
Continuity mistake: Near the end, when the Doctor is explaining to Amy that she will forget Rory when the crack in time is finished eating him because he's part of her personal timeline, and he has his hands on her temples, Amy's hair is covering her ears in some shots, but not others.