The Impossible Astronaut - S6-E2
Visible crew/equipment: Just after Amy comes out of the bathroom, a boom mic can be seen popping up behind the agent's shoulder. (00:28:55)
Revealing mistake: In close-ups of the modified pig, seams are visible on its forelimbs. (00:22:45)
Character mistake: When the news broadcast on the destruction of Henrik's is shown, the chyron misspells the store's name as "Henrick's." (00:07:50)
Evolution of the Daleks (2) - S3-E5
Revealing mistake: When Dalek Sec picks up the remains of the radio and turns it in his hands, the "Hamilton" label on the front of the radio is written backwards, indicating that the shot has been flipped horizontally. (00:05:00)
Trivia: At the beginning of the scene where Clara persuades Rigsy to give her his chronolock, a poster can be seen on a wall in the background, reading "DeLorean" (a Back to the Future reference) in Aurebesh (the writing system from Star Wars). (00:25:00)
The Sound of Drums (2) - S3-E12
Continuity mistake: When gassing the cabinet members, the Master puts on a gas mask. The Valiant logo is above the tube, and upside down. In the next shot, it is below the tube, and the right way up. (00:04:50)
Visible crew/equipment: When the Doctor is painting the fence and vacuuming the living room, Amy lifts her legs to let the Doctor pass with the vacuum, revealing the transmitter for her mic in her back pocket. (00:07:45)
Continuity mistake: At the beginning, when the Doctor takes Amy to planet One, he holds out his hand for Amy to take hold of when they're about to leave the TARDIS. When you see her from the back, Amy lifts her hand wearing her red fingerless gloves. But when it switches shot and faces Amy from the front, she takes the Doctor's hand wearing no gloves. When she steps out of the TARDIS, her gloves are on again. (00:04:54)
Revealing mistake: In the opening scene the Doctor and Donna are speaking over the phone. The purple phone Donna is holding shows the slot where a cable should be plugged in, but there is none. (00:00:25)
Suggested correction: This shouldn't be considered a mistake. While it's true in real life this phone has a slot for a cable, they're on an alien planet and this is unknown technology. In-universe there's no way of knowing what that slot is for, and there's no reason to think the phone needs to be plugged into anything.
Evolution of the Daleks (2) - S3-E5
Continuity mistake: When Martha is searching for how the Daleks changed the design of the Empire State Building, she is examining the plans for the top of the tower. In the first shot where the new plans are visible, the upper right shows a more detailed picture of a plate of Dalekanium. Seconds later, when we can see the new plans again, it's the same side view but the enlarged picture of the plate with the Dalek bumps is gone. These are still the same new plans (the old plans are on her right) and there was no time or reason for Martha to take another page. (00:24:40)
The Vampires of Venice - S5-E6
Revealing mistake: When the Doctor begins climbing a pillar on top of the bell tower, we can see white sky on the central arch. Two other arches in the very same shot show really dark CG sky. (00:42:17)
Continuity mistake: The Doctor is in a room talking to Amy, Rory and everyone else. He sits at a table where there is a house of cards. The house of cards changes between shots. (00:21:56)
Revealing mistake: When the Editor activates the Doctor and Rose's manacles, the right manacle binding Rose's wrist snaps open as they are shocked. (00:35:12)
Visible crew/equipment: As Sally enters the living room in the abandoned house, in the shot where she walks through the doorway, a cameraman holding the camera can be seen reflected in the window of the door next to her. (00:00:35)
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.
Flux: Chapter One - The Halloween Apocalypse - S13-E1
Continuity mistake: At the very start, when Yaz says, "Oh yeah, we are totally in command," just as it begins to zoom out, the handcuff around Yaz's right wrist has the double bar facing out and her left wrist has the single bar facing out, but in following shots both handcuffs are facing the same way. Similarly, this occurs with the Doctor's handcuffs around both wrists, when the Doctor keeps trying the voice recognition. (00:00:10)
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)
The Snowmen - S7-E7
Continuity mistake: When the Doctor offers Clara a TARDIS key, he's holding it differently between shots. (00:44:35)
Continuity mistake: When the Doctor hands out of the base manuals to the expedition crew for the dream test, Albert Smith is shown with his manual open in shots from behind him several shots before he's shown opening it in a shot facing him. (00:35:56)
Dark Water - S8-E11
Continuity mistake: As Clara nods and says "Fair enough" when she thinks the Doctor has told her to leave, her arms go from crossed to by her sides between the closeup and the wide shot. (00:14:29)