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 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. Clearly the use of a double to avoid giving the reveal away too early.
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: The question to unlock one of the doors asks for the next number in the sequence 313, 331, 367. The Doctor gives the answer as 379 with a convoluted (albeit correct) explanation of happy primes, but there are much simpler solutions. The difference between the first and second numbers is 18 and the difference between the second and third is 36 (which is 2 x 18), suggesting that the difference between the third number and the next could be either 54 (= 3 x 18), giving 421 as the next number, or 72 (= 2 x 36), giving 439. It's likely that the Doctor would see that the answer is ambiguous, and yet he confidently states that the most complicated answer is correct. (00:08:45 - 00:09:15)
Suggested correction: If you know what a happy prime is, like the Doctor does, it might be simpler than your idea because you gave 2 options - 421 and 439. The idea of a pattern is there should be only one answer that fits, which would be the case if they're all happy primes.
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)
Factual error: The Olympic torch relay is presented as if there is only one runner carrying the torch through the entire city of London to the Olympic stadium to light the cauldron. Furthermore, when the torchbearer collapses, the TV announcer reacts as if it is now impossible to get the torch to the stadium, just before the Doctor steps in and picks it up. Any broadcast of any Olympic opening ceremonies would show that that's not how the torch relay has ever worked.
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.
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 Time of Angels (1) - S5-E4
Other mistake: At the end when the Doctor is seen shooting the gravity globe, he does not actually move his finger but the pistol still fires.
Continuity mistake: At the end, when the Doctor is watching his hand starting to glow, shots from his point of view show that he's holding it vertically. But shots from the opposite view show that he's holding it horizontally. (00:43:39)
