Other mistake: When the Doctor tells the Atraxi "Oh, you're not the first lot to have come here, there have been so many," one of the monsters shown from their scan of Earth is a group of Ood. Even if in one of their uprisings they attacked the Earth, it would have been in the far future. The Doctor has had no encounters with them on Earth, and he knows them to be peaceful, so why would they be amongst the aliens who have threatened the planet? The only Ood who has been to Earth at this point is Ood Sigma, and he didn't come to attack. In addition, a group of Hath is also shown. These aliens have never been seen on Earth at all. (00:53:30)
Other mistake: When Amy's age is given as 1306, the computer screen reads 1308 instead. (00:15:50)
Other mistake: Joan puts her stethoscope in her ears backwards when listening to John Smith's single heart.
Other mistake: After the Doctor tells Bill that Heather's face isn't symmetrical, when he and Bill look into the "puddle" together the Doctor explains that instead of seeing her normal backwards reflection, she's seeing her face "the right way round." The problem occurs in the next shot of the Doctor and Bill seen in the puddle, because the "WOW!" patch on Bill's jacket is properly where it should be, but note everything else is actually backwards. Things such as Bill's color-block top and her denim jacket buttons are on the opposite way. Also note the Doctor's ring has switched hands. Presumably this shot was edited, and the "WOW!" patch was blurred on the left of Bill's jacket then digitally added to the right side, to give the appearance that it's "the right way round" as the Doctor said. (00:20:15)
Other mistake: When Miss Hartigan is testing the earpod control, the men start off facing her. She instructs them to turn to the right. They turn 90 degrees clockwise. She then tells them to turn to the left. They turn 180 degrees anticlockwise. However, they should have only turned 90 degrees anticlockwise, and end up facing her again. What they actually do is turn on the spot, as opposed to turning left. It takes a further instruction from Miss Hartigan for them to face her again. (00:24:57)
Other mistake: The security guards shoot away the lock on the door, which they then kick down with no real effort. But the door would still be held in place by the hinges - they don't kick it with enough force to rip the hinges out, and even if they had, we can see that there's no damage on the hinge side of the door anyway to demonstrate their forcible removal. (00:24:20)
Other mistake: At the end, the Doctor and Rose treat Charles Dickens by making the TARDIS dematerialise in front of him. The engines begin to grind, but the time rotor (the thing in the console's central column that goes up and down when the TARDIS is flying) does not move. (00:42:53)
Other mistake: When Jenny does somersaults through the laser beams, the last two beams are level horizontally and the higher beam is lower than her foot, so she should have broken it.
The Impossible Planet (1) - S2-E11
Other mistake: When the Doctor asks what the planet is called, Ida says, 'Don't be stupid, it hasn't got a name, how could it have a name?' A few minutes later, she tells the Doctor the planet is called 'Krop Tor'.
Other mistake: The Doctor says "These are a sort of mark 2, yeah?" The subtitles say "These are a sort of Mach 2, yeah?" (00:17:40)
Other mistake: O'Donnell imitates another character retching. The subtitles show this as (WRETCHES). (00:03:00)
Other mistake: Prentis says "In my ship, I have directions to my planet and a selection of items that you can oppress me with." The subtitles say "[...] appraise me with." (00:06:25)
Other mistake: Martha falls into the bog and Hath Peck rushes down to help her. She calls out "Help me, Peck!" but the subtitles read "Help me peg!" This is just one of many errors in this series' subtitles, which seem to have been added by listening to the dialogue without reference to the script. (00:26:30)
Rise of the Cybermen (1) - S2-E8
Other mistake: When the Doctor finds the crystal and blows on it, it glows brightly. While it lights up his face as it should, the backs of his hands light up, apparently from the crystal. This is not possible, as the light comes from in front when the crystal is inside the Doctor's hands. (00:14:55)
Other mistake: When Mickey is trying to pull away from the trash bin, you can see his shadow on the front of his car, but the sun is shining from behind him and the car.
The Wedding of River Song - S6-E14
Other mistake: When the Doctor walks into the control room at the base, the time on the computer is frozen between 5:02:57pm and 5:02:58pm. The Doctor grabs River's hand, and time begins moving up to 5:03:00pm before he is restrained. Later, when the Doctor and River kiss and time begins moving again, the time is 5:02:00pm.
Other mistake: When Sally is taking the key from the angels, she squats down out of the frame to reveal an angel behind her that has lowered its hands from its face. When the shot cuts back to Sally, there is another angel standing in front of the window on the other side of the room whose hands are also lowered from its face. The two angels with lowered hands are directly across from each other: they should have been frozen in place from this point due to their quantum lock.
Other mistake: When the Doctor gets George's psychic cry for help, he's shown reading the message without opening the wallet containing the psychic paper. This despite the fact that all previous instances of the Doctor receiving psychic messages this way has required him to open the wallet, suggesting that the wallet itself does not display the message. (00:02:02)
The Time of the Doctor - S7-E17
Other mistake: While looking around the Doctor's room, one of the children's drawings Clara passes by has the TARDIS in it... when the TARDIS has been absent for all of the 300 years the Doctor has spent on Trenzalore up to this point, so none of the pictures existing now should have the time machine present. And it's not a particularly weathered picture, either, suggesting it can't be from the beginning of his stay on the planet. (00:31:47)
Other mistake: After the Doctor regenerates, there's a close-up of the Thirteenth Doctor's eye with the console room reflected in it. The reflection is the same orientation as a shot from behind her immediately prior, which should not be the case. Take note of the positions of the door and time rotor in both shots. (01:00:45)
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.