In the Forest of the Night - S8-E10
Continuity mistake: When Clara is looking at the drawing in Maebh's homework book while the Doctor tells her about the solar flare, her grip on the book changes between shots. (00:22:44)
Continuity mistake: During the early scene with the Cybermen outside St Paul's, when Missy pulls out her phone/disintegrator weapon and shows the Doctor pictures of the Cybermen going viral all over the planet, and when she prepares to take a picture of the two of them, her grip on the device, as well as which hand she's holding it in, keeps changing between shots. (00:03:00)
Continuity mistake: When Missy orders her Cybermen to blow up the plane and kill some Belgians, her control bracelet is missing from her wrist in one shot. (00:33:54)
Mummy on the Orient Express - S8-E8
Continuity mistake: When the Doctor phones Clara and discovers she's trapped in the locked car with Maisie, his phone keeps switching hands. (00:21:55)
Factual error: After PC Forrest is killed by the Boneless, her nervous system is flattened and displayed on the wall, appearing as a mural. However, there are far too many nerves around where her liver would have been and not nearly enough around her brain.
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)
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)
Revealing mistake: During the sequence where the Cyber-clouds covering Earth are burned away, there is a shot showing the clouds burning over the Sydney Opera House. The shot is, very obviously, a still image to which CGI of the burning sky has been added, with extremely unconvincing results. (00:47:37)
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)
Deep Breath - S8-E1
Continuity mistake: Vastra hands the police inspector a bag of sonic lanterns, to be used to contain the T. Rex. In the next shot, looking at the TARDIS on the riverbank, he's not holding it. (00:02:15)
In the Forest of the Night - S8-E10
Continuity mistake: When Clara mentions worrying about a witch in a gingerbread house while she and the Doctor are searching for Maebh, the phones she is holding switch hands between shots. (00:20:11)
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 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)
Dark Water - S8-E11
Plot hole: When the Doctor and Missy, the latest incarnation of the Master, meet for the first time, she passes herself off as an android. Only later in the episode, after seeing the Gallifreyan hard drive that she has been uploading human minds to, does the Doctor realise that she is a Time Lady, and he doesn't realise that she's the Master until she tells him in the episode's cliffhanger ending. The problem here is that over the show's long history, Time Lords have been shown to have the ability to recognize each other instantly, an ability that makes perfect sense given their powers of regeneration. Previously in the new series, it was even stated that Time Lords can psychically sense each other, an ability demonstrated on-screen in "The End of Time." In "Dark Water", this does not happen, at all. Now, the Master has a history of using technology to block his/her psychic signal before - the Archangel satellite network from Series 3. However, at no point in this episode or the next one, "Death in Heaven", does either the Doctor or the Master even mention such technology as being used, leaving the mystery of how the Doctor didn't recognize Missy as a Time Lady at the very least a rather glaring hole.
Revealing mistake: During the scene at the beginning where people are taking pictures of themselves with the Cybermen, there are a few moments where the Cybermen's armour is revealed to be rubber when people touch it. (00:02:45)
Visible crew/equipment: On the Moon's surface, the camera and boom mic can be seen reflected on the visor of the astronaut as she talks to Clara.
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)
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 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)
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)
Chosen answer: 1) When Stephen Moffat took over he ignored a lot of what had been developed before (there is not in-universe answer). 2) It would have killed Rose, so the Doctor absorbed the energy. His body regenerated before the energy could do a significant amount of damage that would prevent regeneration.