The Snowmen - S7-E7
Continuity mistake: When the Doctor is explaining what the intelligence in the giant snow globe is, though enclosed, the amount of "snow" alternates from a fair mass to a few handfuls and back several times.
Visible crew/equipment: As the black suited figure stops to look at Martha, the crew and equipment are reflected in the helmet and visor. (00:02:30)
Visible crew/equipment: After the acting Prime Minister gives orders to the sergeant and the lift doors close, the soldier turns around. As he issues orders, the boom mic is reflected on his goggles. (00:05:25)
Revealing mistake: When Jex's ship explodes, we see the smoke drifting over town. But it's really obvious that the smoke is coming from the next street, not miles away where Jex's ship is. (00:42:06)
Revealing mistake: In the Torchwood building, a large group of Cybermen start shooting at the Daleks and the Genesis Ark. The Daleks shoot several of them, and you can see a Cyberman that, thanks to hilarious CGI, just collapses like a sock without any physical regard that he is wearing tough metal leg armour, is floating a little off the ground, and falls way too fast than physical laws could allow. (00:25:15)
Other mistake: The Doctor says: "He's taking the suspended-animation chamber to the church." The subtitles say "[...] to the judge." (00:15:30)
Other mistake: Clara says "The dark, the sword, the forsaken, the temple." The subtitles say "The Doc [...]." (00:22:10)
Other mistake: The Fisher King says "The Time Lord... Lied." The subtitles say "The Time Lord... Night." (00:35:00)
Other mistake: The line spoken is "You mash up Vikings to make warrior juice." The subtitles say "You must have [...]." (00:12:30)
Revealing mistake: In several episodes of season 9, starting at "Under the Lake" and continuing through "Before the Flood", "The Girl Who Died" and "Sleep No More", the same white hallway model is used. For the first two episodes, this makes sense, since they play in the same location. However, the same hallway is used in "The Girl Who Died", when the men from Ashildr's village get blasted to death, and again in several scenes in "Sleep No More" when the characters run through the hallways. Also, it seems the control room from the underwater research center, where the characters hide from the ghosts in "Under the Lake" and "Before the Flood", is reused as the white room in "Hell Bent" when the Doctor pulls Clara out of her timeline, though in "Hell Bent" the room is nearly empty and the room in "Under the Lake" and "Before the Flood" is full of equipment.
Revealing mistake: At the end when the Doctor makes it snow, in the wide shot you can see the snow blows in from the left side, showing that they used a snow machine just off-camera. (00:54:30)
Revealing mistake: When the Doctor goes to toss the trio of Christmas balls up, the two times after the first toss are re-used shots of the first toss. His movements of his right arm to bring up the controller are too exact to be coincidence. (00:50:15)
Visible crew/equipment: As the Doctor tries to get Donna to jump to the TARDIS, as the camera is in a close up on her in the taxi, the yellow camera vehicle is reflected on the cab's paint. (00:12:50)
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)
Other mistake: As the Doctor passes a stack of three cubes, the camera is close enough to see the top cube has two small squares intertwined on the side facing diagonally toward the light. He said all were the same, no difference or individuality whatsoever. (00:03:53)
Continuity mistake: As the Doctor talks to Idris/TARDIS, he reaches into his coat. When the angle changes, he reaches in again. (00:18:20)
Continuity mistake: After River shoots the last of the Silence, she turns her gun flat side out, and muzzle up. After the angle change, she does it again. (00:37:58)
Continuity mistake: When the file with the photo of Amy's arm lands in the circle, the thumb in the photo is above the 'T' in 'THIS'. A moment later, the photo's position has turned 180° so that the thumb in the photo is pointed the other way. (00:02:57)
Revealing mistake: As Amy stands where she is told, a cable comes towards her feet. As it does, a black thread can be seen pulling it up to wrap around her leg. (00:21:39)
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.