Continuity mistake: When Emma tells Clara not to trust the Doctor, the position of her hands and fingers, holding her teacup, change between shots. (00:19:00)
Factual error: The Doctor says that the Earth is six billion years old, which is one and a half billion years over - it's only 4.5 billion years old. (00:21:25)
Continuity mistake: When the Doctor puts on a harness during the preparations to rescue Hila, a flap on the front keeps switching between being straight out and being folded behind the strap it's attached to. (00:29:25)
Continuity mistake: When Clara shakes the TARDIS' doors, demanding it let her in, her hands change position between shots. (00:36:25)
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.
Journey to the Centre of the TARDIS - S7-E12
Continuity mistake: When Clara asks the Doctor if he's putting the TARDIS on basic mode because she's a girl and he responds "No!", his hand moves from raised to resting on the console between shots. (00:01:39)
Journey to the Centre of the TARDIS - S7-E12
Continuity mistake: Before they enter the damaged TARDIS, when the Doctor watches Gregor put down Bram, and then asks Tricky why he's using a blast suit and respirator despite being an android, his hands are clasped in front of his chest in close-ups, but down below his waist in wide shots. (00:09:15)
Journey to the Centre of the TARDIS - S7-E12
Continuity mistake: In the storage room, when Clara takes a model of the TARDIS down from a shelf, how she's holding it changes between shots. (00:12:10)
Journey to the Centre of the TARDIS - S7-E12
Continuity mistake: When the Doctor begins to explain to Gregor that the TARDIS doesn't actually have a self-destruct, he places his right hand on Gregor's shoulder. In the next shot, his right arm is by his side and he isn't touching Gregor. (00:26:00)
Journey to the Centre of the TARDIS - S7-E12
Continuity mistake: When Gregor hands Tricky the patch from his jumpsuit, Tricky's hold on the patch changes. In addition, the patch is sagging in shots facing Tricky, but not in the close-up of it. (00:32:40)
Journey to the Centre of the TARDIS - S7-E12
Continuity mistake: Near the end, when the Doctor picks up the remote control and reads the words written on it, the position of his hands as he's holding the device changes between the close-up and the wide shot. (00:43:40)
Journey to the Centre of the TARDIS - S7-E12
Continuity mistake: When the Doctor is asking Clara if she feels safe in the last scene, most of her hair is draped over her left shoulder. However, whether some of her hair is draped over her right shoulder or not changes between shots. (00:45:05)
Continuity mistake: During the sepia-toned explanation of the Doctor and Clara's initial investigation into Sweetville, when they pose as a married couple to infiltrate the place, are accepted, and the Doctor says "The missus and I couldn't be more chuffed, could we love?" in a bad Northern accent, Clara's fake smile goes from closed-mouth to open-mouth between shots. (00:19:57)
Revealing mistake: Just before Strax leaves grumbling that he's going to play with his grenades, if you look closely you can see his face mask peeling. (00:27:45)
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.
Plot hole: At the beginning, when the Doctor, Clara, Angie and Artie get off the TARDIS, the two kids are absolutely convinced that they're on the Moon, despite the Doctor explaining that they're actually at the Spacey Zoomer ride on Hedgewick's World, the greatest amusement park in the universe. The kids only realise they really aren't on the Moon when Webley emerges from inside of a fake rock formation, followed by the soldiers. The part of the room that the soldiers come from, which should have been fully visible to the time travellers from the beginning - in fact, they should have been looking directly at it when they leaned out of the TARDIS in the very first shot - looks nothing like the Moon and contains a sign for the Spacey Zoomer ride and a large map of the amusement park. (00:00:01 - 00:00:45)
The Name of the Doctor - S7-E15
Continuity mistake: When the Doctor pulls the Intelligence's hand off his chin, Simeon's thumb is suddenly no longer touching his face. (00:25:56)
The Name of the Doctor - S7-E15
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)
The Day of the Doctor - S7-E16
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)
Suggested correction: The evidence to this is merely a sign directing people to the scrapyard. This does not indicate whether or not the scrapyard in question is actually at the end of that road.
That still seems to be a point to bring up. Or better yet, "Her address is the same as the scrapyard on that sign outside the school."
The Day of the Doctor - S7-E16
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)
Suggested correction: Perhaps they didn't see everything and only focused on small things, or they remembered the Futurama episode with an amusement park set on the moon.