Continuity mistake: When the Doctor is looking at Rose's hands, turning them over repeatedly, while she's describing how she was hanging from a barrage balloon, there's one moment where her hands are turned palm-up in a shot facing her, but back-up in a shot facing him. (00:18:25)
Continuity mistake: During the Doctor and Nancy's conversation at her hideout, in shots facing her there is a bright circle of light cast on the wall to her left, which her shadow partially overlaps. In shots facing the Doctor where both him and Nancy are visible, the circle is gone, and Nancy's hideout is noticeably more dimly lit. (00:23:15)
Continuity mistake: When Rose and Adam are in his workshop talking about aliens, during the exchange where she asks him about people who claim they've been in spaceships and he responds that he thinks they're nutters, Rose is poking around with her right hand at a storage shelf on the wall before moving her hand to a pile of boxes stacked on a table. When the scene cuts to a close-up of her, her hand has jumped back to the shelf. (00:12:40)
Revealing mistake: There are some moments during the scene where the Doctor is being strangled by the Auton arm where it's fairly obvious that Christopher Eccleston is holding the arm to his own throat. Namely, the moments where the hand isn't quite in the right position, slipping towards his chin.
Continuity mistake: After the Doctor freezes the Auton arm, its index and middle fingers are curled, while its ring and pinky fingers are straightened. When the Doctor and Rose are in the stairwell, most noticeable when they emerge at the bottom, the fingers of the arm are now all slightly curled.