Continuity mistake: At the beginning, when the Doctor asks Martha if they saw her face, her hands change position, from grabbing his arms in a shot facing her to facing up in a shot with both of them. (00:00:10)
Continuity mistake: When the Doctor says, in response to Martha asking how the Family can follow them, "Stolen technology. They've got a Time Agent's vortex manipulator," in a close-up of his face he reaches with his left hand for a control on the console, but in a following shot of his hands, they're right next to each other. (00:00:25)
Continuity mistake: When Martha and Jenny are washing the floor, just as Hutchinson and Baines come along and tell them off for laughing, one of the lace ribbons on Martha's cap moves between hanging in the back in shots facing her and draped over her shoulder in shots facing the schoolboys. (00:04:15)
Continuity mistake: When Martha initially bursts into John Smith's study after hearing that he fell down the stairs, the door is mostly closed. When she runs back to the door to knock on it after Joan Redfern tells her off for bursting into a master's study unannounced, the door is open wider. (00:06:35)
Continuity mistake: During Joan's encounter with the Family's spaceship, when it shines a beam of green light at her, she shields herself by raising her right arm. It changes position between a wide shot and a close-up. (00:12:20)
Continuity mistake: After watching the Family's spaceship land, Jeremy Baines puts his hand on a tree stump as he walks around it to approach the ship. He does this twice, in two successive shots. (00:14:10)
Continuity mistake: When the Doctor fits the Chameleon Arch watch into the headset, his hands change position between shots. (00:20:15)
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.