Continuity mistake: When Clara tells Maisie that "Difficult people can make you feel all sorts of things", as she finishes the sentence the view cuts from a close-up of her to a wide shot, and the light and shadows cast onto her face change with it. (00:17:20)
Other mistake: While looking around the Doctor's room, one of the children's drawings Clara passes by has the TARDIS in it... when the TARDIS has been absent for all of the 300 years the Doctor has spent on Trenzalore up to this point, so none of the pictures existing now should have the time machine present. And it's not a particularly weathered picture, either, suggesting it can't be from the beginning of his stay on the planet. (00:31:47)
Continuity mistake: When the Doctor teleports onto the Dalek ship and announces himself, he's holding up a broken Dalek eyestalk in the wide shot as he throws off his hood, but then in the close-up he throws the hood off again, with his arm lowered. Then he raises his arm again, with his arm bent at the elbow, only for a wide shot to have his arm sticking straight up, with his elbow straight. (00:00:55)
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: 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)
Continuity mistake: When the Doctor, being held by two of the crewmen, explains that there's a geographical anomaly the sub can land on to halt its descent, the hand of the crewman holding his right arm disappears in a close-up, followed by the crewman himself disappearing in the next shot. (00:04:57)