Continuity mistake: Davros' chair has metal parts which go over his shoulders - they are attached to the chair, not Davros. When the Doctor steals Davros' chair they disappear, but when Davros is back in it they have reappeared.
The Angels Take Manhattan - S7-E6
Continuity mistake: As the Doctor explains about the book he's reading, he goes from holding it with one hand to two between angles. (00:07:19)
The Impossible Astronaut - S6-E2
Other mistake: After River shoots at the astronaut going into the lake, she drops her arm. The next second, she turns around and the gun is holstered without her having made any movement to do so, and there was no sound made.
Suggested correction: The holster is low enough for the subtle movement her right arm makes to be using it. As for the sound, the removal of her gun doesn't make a sound either. The only sound heard is directly before it when she put her medical scanner away.
Continuity mistake: The Auton in the red shirt is seen starting to come down the escalator, then at a quarter of the way down, then at the top again, just starting down.
Visible crew/equipment: Just after Missy treads on Osgood's glasses after killing her, you can see a boom mike shadow on the wall.
Factual error: In this episode, it is stated that the Moon's sudden increase in mass caused a devastating global high tide. The amount of the increase in mass is given as 1.3 billion tonnes. But the Moon has a mass of over 70,000,000,000 billion tonnes, or over 50 billion times the supposed increase. Such a negligible increase in mass, less than 0.000000002%, would have almost no effect on Earth's tides, let alone be devastating. (00:20:46)

Continuity mistake: When Robin Hood has finished introducing the merry men to the Doctor and Clara, Clara says "You really are Robin Hood and his merry men" and she is shown with her arms parted away from each other. In the next shot, her arms are suddenly closer to her. Then in the next shot, her hands are now closed together. (00:08:25)
The Day of the Doctor - S7-E16
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: The submarine surfaces among icebergs at the end. Just as the others go back into the submarine, the Doctor stays up there. Some snow goes onto his lip and his hair. In the following shot, we can see he isn't moving. But in the next shot, the snow on his hair and lip isn't there anymore. (00:40:00)
The Impossible Astronaut - S6-E2
Visible crew/equipment: The astronaut coming out of the lake is seen twice in series 6: In episode 1, "The Impossible Astronaut", and in episode 13, "The Wedding of River Song." In "The Wedding of River Song", when the helmet of the suit is lifted the astronaut is revealed to be River Song. However, in "The Impossible Astronaut", when the helmet was lifted, a man's beard can be seen. Since it is a man in the suit, then it was just a double seen in "The Impossible Astronaut."
The Angels Take Manhattan - S7-E6
Other mistake: The photo shoot PA from "Asylum of the Daleks" earlier in this season isn't in the credits for that episode, but is credited in this episode, despite not featuring in it. (00:45:36)
Factual error: When the Doctor, Amy and Rory are on the roof and the Doctor says "The question for now is total event collapse means that every star in the universe never happened", the Gherkin can be seen in the background. However, the Gherkin wasn't built until 2003, whereas this episode takes place in 1996. (00:22:40)
Revealing mistake: In the museum after the Doctor, Amy, young Amy and Rory escape the Stone Dalek, the Doctor uses the Vortex Manipulator to go back in time to tell Rory in 102 AD to let him out of the Pandorica. The third time he goes back, Amy moves despite being dead. (00:19:38)
Revealing mistake: When the landlord, Purcell, wakes up on his floor because his pet dog is licking his hand, we see a few pieces of dog food fall from his fingers - should have been a re-shoot, but all credit to the actor, he knows it has happened and is quick to hide them again. (00:38:38)
The Girl in the Fireplace - S2-E7
Continuity mistake: When Rose is giving the 5 year warning to Reinette, she's got a noticeable spot on her chin. When Reinette goes behind the tapestry and sees the ship, Rose's spot has suddenly vanished. (00:28:50)
Character mistake: After the Carrionites kill Lynley, the Master of the Revels, by using the doll to make him drown on dry land, the Doctor says, while examining the body, that he's never seen a death like it. In the Third Doctor serial "The Mind of Evil", involving a monster that could make people relive their worst fears, a character died in exactly that fashion. (00:13:10)
Revealing mistake: In the underground scene in the Nestene lair, the CGI used to create the Nestene is horrendous. And in a shot from behind the Doctor, the Nestene looks like a whole bunch of orange pixels.
Other mistake: When Mickey is trying to pull away from the trash bin, you can see his shadow on the front of his car, but the sun is shining from behind him and the car.
Revealing mistake: Most of the time, the eyes of the dummies are molded and opaque. But in the mall, there are small holes in the eyes.