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)
Continuity mistake: When the Doctor is talking to River just before entering his own timeline to rescue Clara, in the shots facing him, the glowing column representing his timeline is not visible, despite the fact that a wide shot reveals he's standing right in front of it. (00:39:25 - 00:40:04)
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.
Other mistake: When Mr. Thursday goes to see Vastra, to hire her to investigate his brother's death, he doesn't see her face (she's a Silurian "lizard woman from the dawn of time") until she lifts her veil to take a closer look at a photograph he brought her, upon which he faints. However, Vastra's veil is quite see-through, enough that her non-human appearance is obvious to the audience even before she lifts it. The same thing happens when she goes to visit the coroner later - although he doesn't faint.
Continuity mistake: When Clara draws the Doctor's attention to the vision of a forest appearing in the archway, the candelabra she is holding has two candles in it, with the third hole empty. Moments later, after the apparition has disappeared, there are now three candles in it. (00:15:30)
Continuity mistake: For most of the episode, there is a thunderstorm going on at Caliburn House. However, when the TARDIS is seen dematerializing and rematerializing when the Doctor and Clara go to take pictures of the ghost throughout time, it's dry in the grove where it was parked. The first time is especially noticeable, as moments later we are shown Professor Palmer and Emma looking through a rain-spattered window, commenting on the noise of the TARDIS' engines.
Continuity mistake: When the Doctor and Clara are sitting at their table on the balcony, talking, the level of Clara's mostly-finished milkshake changes several times, most noticeably when she and the Doctor are arguing over who is going to use her computer to hack the bad guys' systems. (00:31:00)
Continuity mistake: When the Doctor and Clara, while seated at their table on the balcony, are arguing over who has the better hacking skills while pulling her computer back and forth, in overhead shots their table is somewhere in the middle of the balcony. This contrasts with all other shots, which show their table right next to the railing. (00:31:16)
Revealing mistake: When the Doctor and Vastra are on the TARDIS talking about Clara's injuries, and he says that he thinks for once the universe owes him one, he pulls some switches on the console. If you pay attention, you'll notice that the console wobbles slightly as he does so. (00:49:48)