Other mistake: Joan puts her stethoscope in her ears backwards when listening to John Smith's single heart.
Revealing mistake: In the close up shot of the boys' machine guns firing, in the background a white truck can be seen driving across the green countryside; not appropriate for the time period of the story. (00:25:25)
Plot hole: The Doctor leaves Martha a recording with instructions for her for when he's human. However, the flashbacks to the incident that led to him using the Chameleon Arch don't leave enough - or any - time for him to have made the recording, presenting his decision to use the device as a spur-of-the-moment one that he immediately acts upon.
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)
Suggested correction: He would have been planning the change to human for a while now, not just made it up on the fly. So he could have made a recording before the opening scene.
The episode makes it pretty clear that he and Martha got taken by surprise by the Family's attack. The Doctor also explicitly says, when he gets out the Chameleon Arch headset, that he never thought he'd use it. The flashbacks consistently present his decision to become human as one made as an urgent, in the moment one.