Continuity mistake: When Clara shakes the TARDIS' doors, demanding it let her in, her hands change position between shots. (00:36:25)
Continuity mistake: While Emma is explaining to Clara what an empathic psychic is, the Doctor grabs a bottle of milk from the table and takes a swig out of it, holding the bottle in his right hand, before jumping into the conversation to state that empaths are both extremely compassionate and extremely lonely. While he's saying this, his left hand goes from gesturing in a close-up to holding the milk bottle in a wide shot. (00:06:25)
Continuity mistake: When Emma tells Clara not to trust the Doctor, the position of her hands and fingers, holding her teacup, change between shots. (00:19:00)
The Bells of Saint John - S7-E8
Continuity mistake: While the Doctor and Clara are talking and realise that she now possesses extensive computing knowledge, in shots facing the Doctor he has his hands raised in various gestures or by his mouth, but his hands aren't visible in shots facing Clara. (00:23:13)
The Bells of Saint John - S7-E8
Continuity mistake: When the Doctor says "I'm an alien from outer space, I'm a thousand years old, and I can't fly a plane! Can you?", the sonic screwdriver jumps from his right hand to his left. (00:26:43)
The Bells of Saint John - S7-E8
Continuity mistake: When Clara takes the copy of Summer Falls away from Artie briefly, the position of her hand on the book changes between the initial shot and the close-up of the book's cover. (00:05:41)
The Bells of Saint John - S7-E8
Continuity mistake: When Clara asks the "girl" coming down the stairs if she's a friend of Angie's, and the "girl" replies in a monotone, in the shot facing Clara the girl-robot is seen nearly at the bottom of the steps, but in the next shot facing the "girl", she's suddenly higher up the stairs. (00:13:07)
The Bells of Saint John - S7-E8
Continuity mistake: When Clara is asleep in bed after the Doctor prevented her from being downloaded by the people in the Shard, he sets up a vase of flowers, a glass of water and a plate of Jammie Dodgers on her bedside table. The positions of the glass, the cookies on the plate, and the torn-open package the cookies came out of is seen when the Doctor leaves a half-eaten cookie on the plate in a close-up. When Clara wakes up, however, the cookies on the plate, the packaging and the glass have all changed positions. (00:19:20)
Revealing mistake: When an Atraxi ship appears over the village green, there's a shot where the Doctor, Amy and Rory turn to look at it, and they're standing in bright sunshine with their shadows visible - despite the fact that the Atraxi have surrounded the planet with a forcefield that dims sunlight, so those shadows shouldn't be possible. (00:36:05)
Continuity mistake: When the Doctor throws his hands in the air and exclaims, "Who da man!?", Rory's phone, which he was holding in the shots immediately prior, is missing. (00:47:25)
Continuity mistake: After Prisoner Zero is taken away, when Rory asks the Doctor if everything is back to normal, the Doctor is holding Rory's phone in his right hand while dialing a number. In the shot immediately after, focusing on Rory, where the Doctor walks by him and lightly smacks him on the shoulder, the phone is suddenly in the Doctor's left hand. (00:50:20)
Continuity mistake: When Amelia comes out of her house with a torch to look at the crashed TARDIS, its exact position in her hand changes between shots a few times. (00:03:30)
Continuity mistake: After the Doctor spits out some yogurt that Amelia gave him and wipes off his mouth, there's still some yogurt on his face and chin. Immediately afterwards, he involuntarily jerks around a bit due to regeneration sickness, and the yogurt is gone. (00:06:35)
Continuity mistake: At one point while the Doctor is explaining to Amelia what the crack is, there's a shot where he has his hands on the wall examining the crack as he leans over Amelia's desk, then the camera cuts to a shot of Amelia where the Doctor is standing upright with his hands not touching the wall at all. (00:10:15)
Continuity mistake: When Mrs. Angelo and Jeff recognize the Doctor, leading to him learning that Amy was known for drawing cartoons of him when she was younger, he keeps changing position between shots. (00:30:05)
Continuity mistake: When the Doctor finds the stolen cup inside Christina's knapsack, he's shown reaching for it twice, in the wide shot and the close-up. (00:38:40)
The End of Time: Part Two - S4-E18
Continuity mistake: When Wilf takes out his revolver and offers it to the Doctor, he's holding it with the grip pointed toward the Doctor. In a wide shot shortly afterwards, Wilf's arm is moving to hold the gun out again, this time with the barrel closer to the Doctor. In the next shot, a close-up of Wilf, the gun is back to its first orientation. (00:25:20)
The End of Time: Part Two - S4-E18
Continuity mistake: When Shaun and Sylvia run out of the Nobles' house to look as Gallifrey begins to phase in and out next to Earth, Shaun's right hand, which he had on Sylvia's shoulder, changes position between shots just before he runs off looking for Donna. (00:40:40)
Revealing mistake: Adams, the female Vinvocci, has a tendency to wrinkle her forehead, which makes the fact that her spiky head is a cap the actress is wearing very obvious.
The End of Time: Part Two - S4-E18
Continuity mistake: When Donna, on the phone with Wilf, is surrounded by Master duplicates in the alley behind her house, she has her phone to her ear, but there's a shot where she looks behind her to see two Masters, one of whom is wearing a bowtie, entering the alley, her phone is missing, only to be back by her ear in the next shot. (00:07:05)
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.