Deliberate mistake: Looking closely at the floor of Eleven's console room reveals that the part of the floor around the console facing the door has been discreetly raised up, which it isn't in any other appearance of this console room, so that Clara can ride her motorcyle inside it without going down two steps. This wasn't in any previous episode and is gone in the next one.
Continuity mistake: When Clara asks Kate why her two assistants have entered the Black Archive, she rests her left arm on the sill of the window of the containment unit she's inside. In the next shot, when Clara slowly turns to look at "Kate", who's just revealed she's actually a Zygon imposter, her left arm is by her side. (00:39:55)
Continuity mistake: When the Doctors figure out how to disintegrate the door, when Eleven takes out his screwdriver to check the calculation and announces that it's complete, Ten's right hand, with which he's holding his screwdriver, goes from raised at roughly shoulder height to much lower between shots. (00:44:50)
Continuity mistake: When Osgood discovers Kate trussed up where the Zygons left her, when she pulls off the sheet covering her Kate's head is completely covered by a membrane-like mass. Moments later, after Osgood has begun working at Kate's hands to get her free, in the next shot with Kate's head in it her face is now uncovered. (00:46:15)
Continuity mistake: In the scene at the end in the Undergallery, when Ten walks up to the Gallifrey Falls painting, wondering what its actual title is, the door of his TARDIS, visible behind him, is open. In the next shot with the TARDISes visible, the door is shut. (01:10:55)
Revealing mistake: When Osgood tells Kate that they're using Derren Brown as the explanation for flying the TARDIS into Trafalgar Square by helicopter, the two women are standing in front of the TARDIS. Its door is slightly open, revealing an interior that is obviously a picture. (00:05:00)
Continuity mistake: During the scene in the barn where the three Doctors have their hands on the button, when Eleven notices Clara crying and asks her what's wrong, the Doctors' hands go from stacked on top of each other on the button to only touching it with their fingers. (01:02:40)
Other mistake: Billie Piper is listed as playing "Rose" in the closing credits. Rose was certainly mentioned, yes, but Piper in this episode was actually sentient superweapon the Moment, who merely took Rose's form, and was in all other respects nothing like the former companion.
Continuity mistake: Among the various contents of the Black Archive are visible several objects that shouldn't be there, because it is impossible for U.N.I.T. to have acquired them. In particular: A detonation pack from "Planet of the Ood", set in the 42nd century, a few thousand years in the future. The Supreme Dalek's shell from "The Stolen Earth"/"Journey's End" - it was shot and killed by Jack Harkness, destroying the shell. The restraint chair from "The End of Time", last seen on the Vinvocci's ship. The makeshift sonic screwdriver built by the alternate Amy from "The Girl Who Waited", since that version of Amy was wiped from existence. A different explosive carried by Gregor Van Baalen in "Journey to the Centre of the TARDIS", which is both set in the future and involves a complicated situation in which the events ended up technically not happening.
Continuity mistake: After the 10th Doctor marries Elizabeth, they kiss. While they are kissing, the collar on his jacket gets turned up, from her point of view. The camera then switches to look at her from over his shoulder, then back, and now the collar is straight. (00:49:40)
Continuity mistake: At the end, when the Tenth Doctor steps into his TARDIS, there are three sets of cups and saucers on the side of the bench farthest from the TARDIS, and Clara's set in the middle of the bench, but as the TARDIS fades away, there are two sets on each end of the bench. (01:14:10)
Continuity mistake: When the three Doctors have all just come up with a plan to stop Gallifrey being destroyed, the War Doctor shouts "Thank you, Bad Wolf Girl!" At this moment, standing in front of "Rose", the Tenth Doctor's hair is spiked up and messy, but then immediately in the next shot, after the Moment has disappeared, when he questions what the War Doctor just said, his hair is flat and neat again. (01:06:25)
Continuity mistake: In this episode, I. M. Foreman's scrapyard is at the end of the alley next to Coal Hill School. In "An Unearthly Child", the scrapyard was far enough away from the school that Barbara and Ian take Ian's car to get there. Barbara also describes it to Ian as "there's a big wall on one side, houses on the other." If it was right next to the school, she would have mentioned "that scrapyard next to the school." (00:00:15)