Continuity mistake: When Martha is walking up to the hospital just before the motorcycle gear-clad slab bumps into her, her right hand goes from by her side to holding her purse strap between shots. (00:02:15)
Continuity mistake: When Martha is talking to the Doctor, who is posing as a patient, about her encounter with him in the street earlier, which he doesn't remember, she takes her stethoscope off her neck. The camera cuts to the Doctor, then back to her, and she's taking it off again. (00:04:15)
Continuity mistake: Martha reaches her right hand up to open the window, prompting Julia to panic and say "Don't! We'll lose all the air!" When the shot changes as Martha points out that the windows aren't exactly airtight, her right hand is suddenly lowered. (00:09:47)
Continuity mistake: When the Doctor is looking out the window while asking Martha if there's a balcony on the floor of the hospital they're on, in close-ups of him only his right hand is visible, resting on the sill between two windowpanes, and his left arm is by his side. In a wide shot from outside looking in, his left arm is stretched out with his left hand gripping the divider between two windowpanes, in a spot where it should have been visible in the preceding shot. (00:10:05)
Continuity mistake: When the Doctor and Martha open the doors to the balcony, in a shot facing them, Martha lets go of the handle of her door and it swings completely open. In the next shot, from behind, Martha is still holding the doorknob. (00:10:35)
Continuity mistake: When the Doctor is telling Martha that he was just wandering and not looking for trouble, in the wide shot, he's rubbing his chin. In the close-up immediately afterward, his hand has jumped to his hair. (00:19:45)
Continuity mistake: When Martha and the Doctor are talking in the alley at the end, he's leaning on the TARDIS. His exact position keeps changing between shots. (00:39:10)
Continuity mistake: When the Doctor puts his tie back on after returning from the morning, the collar of his shirt is noticeably askew as a result. Just moments later, when Martha enters the TARDIS for the first time, the collar is neat again, without him having done anything. (00:41:00)
Continuity mistake: When the Doctor first enters Shakespeare's room at the inn, the collar of his coat is askew. The scene cuts to Shakespeare, and when it cuts back to the Doctor his collar is now flat, without him having moved his hands from his pockets. (00:09:20)
Continuity mistake: When Lilith has Shakespeare under her spell and is having him write an alternate ending to his play, there is one shot of his face where his quill can be seen in the corner, perfectly still, even though the next shot shows that he's writing. (00:18:25)
Continuity mistake: When the Doctor, Martha and Shakespeare are in the Globe and they talk about the theatre's architecture, there is a wooden staircase in front of the stage, which Martha and Shakespeare use to descend from the stage when the three leave. Shortly after, at the beginning of the scene where the two actors from Shakespeare's company accidentally summon a Carrionite while practicing their lines, the staircase is gone. (00:22:10)
Continuity mistake: When Lilith runs her hand along the side of the Doctor's head to distract him so she can get some of his hair, in the wide shots her fingers are extended past his ear. In a shot facing him, however, her fingers are curled and in front of his ear. (00:34:40)
Continuity mistake: When the Doctor is persuading Shakespeare to come up with some words to stop the Carrionites with, in wide shots he has his right arm around Shakespeare's shoulder and is holding his left arm. In close-ups, they are not in physical contact. (00:38:35)
Continuity mistake: In the episode "New Earth", the Doctor said that the titular planet is in the galaxy M87. Upon returning to New Earth in this episode, he says that the planet is 50,000 light-years from where the original Earth used to be. That's a difference of over 50 million light-years, since M87 is a very real galaxy in the centre of the Virgo Cluster, that far away from the Milky Way. (00:02:55)
Continuity mistake: After Milo and Cheen abduct Martha, they put a sleep patch on her before entering their car. In the close-up where Cheen applies the patch, it's stuck on securely and neatly, with the top and bottom of the square pointing directly at Martha's head and chest respectively. In a wide shot immediately afterwards, the patch is stuck on quite loosely and has gone askew. (00:06:35)
Continuity mistake: After the Doctor gets directions to the motorway, when the red-haired female pharmacist leans over her counter to try and persuade him to buy some Happy, her hands change position between shots. (00:08:00)
Continuity mistake: The registration of Milo and Cheen's car is shown on the computer screen and stated aloud as "4-6-5-◊-6." However, there is a shot of Martha and Cheen looking out the window where the car's registration sticker is visible, showing a different registration: "9-9-6-γ-1." (00:13:15)
Continuity mistake: When the Doctor, after being placed on hold while attempting to call the police, talks to Brannigan and Valerie about other people he could contact, in close-ups, Valerie has her right hand resting on the top of her seat. In a wide shot, she lowers her hand, but in the next close-up of her, it's jumped to its previous position. (00:14:20)
Continuity mistake: When Martha, Milo and Cheen are talking in the powered-down car, the lighting changes between wide shots and individual close-ups.
Daleks in Manhattan (1) - S3-E4
Continuity mistake: When the Doctor turns the newspaper towards Martha so she can read the headline, in the wide shot, the corner in his right hand is bent back towards him. In the close-up showing the headline, the corner is straightened with his hand in a different position. (00:04:29)
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.