The Sontaran Stratagem (1) - S4-E4
Continuity mistake: In the TARDIS as Donna navigates, the Doctor uses a hammer to help correct the trajectory, then rests it on his neck and shoulder. A second later, when the phone rings, his hand, holding the hammer, is suddenly much lower, below his waist level. (00:03:15)
Continuity mistake: The cab Donna's in passes a red vehicle on the bridge. A second later, it's nowhere to be seen looking back. (00:12:15)
The Impossible Planet (1) - S2-E11
Continuity mistake: When Rose, the Doctor, and the others are running across the walkway a stream of steam appears and disappears between shots. (00:03:55)
Visible crew/equipment: When Rose and the Doctor are riding after landing, you see the camera, crew and lighting equipment reflected in their glasses. (00:04:00)
Continuity mistake: When Suki goes to leave the lift on floor 500, her arms are by her sides, then suddenly both hands are gripping the strap on her bag. (00:14:00)
The Day of the Doctor - S7-E16
Continuity mistake: After the 10th Doctor marries Elizabeth, they kiss. While they are kissing, the collar on his jacket gets turned up, from her point of view. The camera then switches to look at her from over his shoulder, then back, and now the collar is straight. (00:49:40)
The Day of the Doctor - S7-E16
Continuity mistake: At the end, when the Tenth Doctor steps into his TARDIS, there are three sets of cups and saucers on the side of the bench farthest from the TARDIS, and Clara's set in the middle of the bench, but as the TARDIS fades away, there are two sets on each end of the bench. (01:14:10)
Continuity mistake: When the Doctor uses his sonic screwdriver on the glass partition in the Torchwood Institute, cracks radiate out in a star pattern, meaning the glass will break into pointed shards. When it does break, it breaks into cubes, like safety glass. (00:29:30)
The End of Time: Part Two - S4-E18
Revealing mistake: When Addams is telling Rossiter not to respond the Master's message, a patch of non-green skin can be seen on her face showing where the makeup wasn't fully painted on. (00:27:50)
The End of Time: Part Two - S4-E18
Revealing mistake: When the Doctor is being rolled down the stairs whilst he is strapped to the chair, it is apparent that in the wide shots, it is a dummy in the chair and not the Doctor. In the wide shots, the Doctor is sitting virtually still and motionless, but in the closer shots, he is fidgiting.
Continuity mistake: When the Doctor is at the Tower of London with Amy and Kate, he claims he needs some air. When Amy follows him she follows him twice, in two different shots. The first time on 'ground view' walking and the second time on 'above view' running. (00:21:20)
Continuity mistake: In the scene where Cobb is briefing his troops, the troops all have their guns, but in the other scene (after you see the Hath marching) the troops are receiving guns. (00:15:45)
The Family of Blood (2) - S3-E9
Revealing mistake: The pyrotechnic mortars used in the destruction of the Family's ship are visible in the shots leading up to their detonation. As the Family run from their ship through the field, the mortars are visible against the branches behind them. Shortly afterwards, they detonate, creating the illusion that the invisible craft has exploded.
Revealing mistake: When the TARDIS dematerialises and causes wind to blow against Churchill and Amy, their clothes are affected - but the cigar smoke in the air is unaffected, and actually drifts towards the vanishing TARDIS. (00:14:25)
Audio problem: Near the beginning of the episode when we first see Bannakaffalata, he says "Christmas is funny", yet his lips don't match what he is saying. (00:01:45)
Continuity mistake: Throughout this episode, Amy's earrings seem to disappear and reappear.
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.