Deep Breath - S8-E1
Continuity mistake: In the restaurant basement, while the Doctor and Clara are looking around while speculating on why the clockwork droids are harvesting organs, Clara moves a chain out of her way with her left hand before releasing it, only to be holding the chain again in the next shot. (00:44:10)
Deep Breath - S8-E1
Revealing mistake: After the clockwork droids shut down, when the ones in the restaurant basement start falling over, the extended blade of one of the toppling droids flops about like rubber. (01:08:15)
Continuity mistake: During Clara's first conversation with Danny, the folders in her hands are unmarked in close-ups, but have labels on them in wide shots. In addition, the folders and newspaper she's holding keep changing position between shots. (00:07:30 - 00:08:26)
Continuity mistake: When Colonel Blue informs the team that radiation levels are getting dangerously high as they head for the Dalek's trionic power cells, the team's location inside the Dalek, shown on a computer screen, changes between shots. (00:25:16)
Continuity mistake: Throughout the episode, the collar of the Doctor's shirt frequently tucks in and out of his coat from shot to shot. Especially noticeable in the scenes where they are looking for and subsequently fix the Dalek's radiation leak.
Continuity mistake: When Clara exits the TARDIS in Sherwood Forest for the first time, she closes the door. Shortly thereafter, when Robin draws his sword on the Doctor, the door has opened itself. (00:04:24)
Revealing mistake: When the old man is stabbed, the sword is retracted and we can see there is no blood visible on the sword. This is visible even before the blood is wiped off. (00:06:55)
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)
Continuity mistake: When Marian attempts to defend a man who's collapsed from exhaustion from the robot knights, when the knight says "Analysis suggests the peasant-creature is spent", the man goes from sitting up to bent over between shots. (00:17:53)
Revealing mistake: When Robin Hood comes up behind the Doctor to push him into the water, it's obviously a stunt double with a bad wig.
Continuity mistake: When Danny is saying "Straight to dinner", the shot switches from one facing him to one facing Clara. In the first shot, Clara is holding up her glass, but in the second shot her glass is suddenly lowered before she raises it again. (00:03:52)
Continuity mistake: When the Doctor shows Clara the "listen" written on one of his blackboards, the handwriting is different to when it was first shown. (00:07:07)
Continuity mistake: After the Doctor is knocked unconscious, Clara uses the psychic circuitry to pilot the TARDIS to what turns out to be a moment in the Doctor's past, in the barn first seen in "The Day of the Doctor." The loft in the barn where the young First Doctor is sleeping in bed, however, was not present in the previous episode.
Suggested correction: These events take place thousands of years apart. Buildings (especially wooden ones) are likely to change in that time.
The barn appears three times, in "The Day of the Doctor", "Listen" and "Hell Bent." Its appearance in "The Day of the Doctor" is chronologically in-between its appearances in "Listen" and "Hell Bent." Both of the two latter episodes have the loft, but "The Day of the Doctor" doesn't. That's the mistake here.
Time Heist - S8-E5
Continuity mistake: After Delphox taps on the glass to awaken the Teller, her fingers close as her hand drops below shoulder level. After the angle change, her hand is above shoulder level, index finger extended. (00:06:03)
Time Heist - S8-E5
Continuity mistake: When the Doctor takes the case with the neophyte circuit out of a safety deposit box and opens it, his hands holding the case change position between shots, being suddenly raised higher in the second one. (00:31:27)
Time Heist - S8-E5
Continuity mistake: Near the end, when the Doctor and Clara are standing by the TARDIS on the planet they took the Teller and its mate to, Clara's hands go from touching the buttons on her jacket to loosely clasped lower down. In the third shot of her, they return to the first position. (00:44:28)
Continuity mistake: When Courtney comes into The Caretaker's room in search of paper towels, there is a "keep out" sign (reading "Go Away Humans") hanging in the window of the inner door. When the Doctor is talking to her just before she leaves, the sign is missing. Over the course of the rest of the episode, the sign proceeds to appear and disappear a few more times. (00:15:50)
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)
Factual error: When Clara is watching the Earth through binoculars in order to see whether people left their lights on or off, the planet is rotating at an impossibly high speed. (00:36:15)
Factual error: Near the end of the episode, the full moon is shown in the daytime sky, well above the horizon. This is impossible, as any celestial body lit by the Sun has its full phase only when it is directly opposite the Sun; thus, a full Moon rises at sunset and sits high in the sky only during the night. For the Moon to be in the sky during the day as shown, it would have to be visibly of a phase other than full.
Suggested correction: The moon is not actually completely full. It's in a gibbous phase (opposite of a crescent), which can indeed be seen in the daytime.