Other mistake: At the end, the Doctor and Rose treat Charles Dickens by making the TARDIS dematerialise in front of him. The engines begin to grind, but the time rotor (the thing in the console's central column that goes up and down when the TARDIS is flying) does not move. (00:42:53)
The Doctor Dances (2) - S1-E10
Factual error: Look closely at some of the freight wagons at 'Limehouse Green' railway station: several of them appear to have 'British Rail Freightliner' livery. This episode is set in 1941, but British Rail did not exist until 1948, and the Freightliner Division did not exist until the 1980s.
Continuity mistake: When Suki discovers the bodies on Floor 500, she drops her flashlight, but in the next shot she's holding it again. (00:15:20)
Continuity mistake: When the Doctor and the housemates in the Big Brother house are watching TV, the brand name of the TV - Sony - appears in some wide shots, but is absent in other wide shots and all close-ups. (00:14:10)
The Parting of the Ways (2) - S1-E13
Continuity mistake: Near the beginning of the episode, the Doctor and Jack destroy a Dalek who is inside the TARDIS. It is seen again later when the Doctor, Rose and Jack come back into the TARDIS after talking with the Dalek Emperor. Yet later when the Doctor is sending Rose home, there is no destroyed Dalek. (00:14:20)
Revealing mistake: At the end of the episode there is a side shot of the Doctor leaving the TARDIS in which you can see inside, but the control room isn't visible, just the side of the police box, with light from outside shining through the window. (00:38:00)
Audio problem: Just after the Doctor makes his appearance and Lynda tells him he's "in the house", she appears to continue talking to him but we never hear what she says; instead the scene cuts to the other two housemates complaining about the Doctor's sudden appearance. (00:01:40)
Character mistake: When the news broadcast on the destruction of Henrik's is shown, the chyron misspells the store's name as "Henrick's." (00:07:50)
Revealing mistake: In close-ups of the modified pig, seams are visible on its forelimbs. (00:22:45)
Continuity mistake: As the Doctor, Captain Jack and Lynda with a Y have been captured, the Doctor turns his head to the right, then after it cuts it shows him turning his head again and saying "Let's do it." (00:32:05)
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: When the Doctor pulls the arm off the Auton and tosses it to Rose, the arm is bent at the elbow and solid plastic, with a smooth, clean break. Later, particularly noticeable when Rose has left the department store, the arm is hollow, with an unbent elbow and a jagged break. The arm continues to change between the two appearances for the rest of its screentime. (00:07:08)
Revealing mistake: When the Editor activates the Doctor and Rose's manacles, the right manacle binding Rose's wrist snaps open as they are shocked. (00:35:12)
Continuity mistake: During the opening montage, showing the Slitheen incapacitated by electrocution, when Margaret drops Indra's body and stumbles back, a close-up of the body on the floor shows her legs without the pulsing electricity covering her entire body, which is visible in other shots.
Continuity mistake: When Harriet Jones is hiding in the closet and spying on the Slitheen attacking General Asquith, wide shots of the closet door have it in shadow, but close-ups of Harriet have the part of her face that is visible illuminated.
Continuity mistake: When Indra Ganesh offers Joseph Green the briefcase with the Emergency Protocols, he's holding it with the handle in his right hand in wide shots, but with it in his left hand in close-ups of him. (00:12:36)
Visible crew/equipment: During the news broadcast on the disappearance of the Prime Minister, shown on an in-universe TV screen, the reflection of the camera filming the TV is visible. (00:12:00)
Revealing mistake: After the Doctor deactivates the signal hiding the Dalek fleet, when the camera zooms out to show the ships, the background image of the Horsehead and Flame Nebulae is cut off a bit below where the Dalek Emperor's flagship is shown, revealing the end of the picture they used for a background. (00:39:00)
The Parting of the Ways (2) - S1-E13
Continuity mistake: At the beginning of the scene where Rose, Jackie and Mickey are in the restaurant, in the wide shot, Rose moves her left hand to the side of her head, while looking down with her head facing towards the other side of the table, which her elbow is resting on. In a close-up immediately afterwards, she's looking out the window with her hand to her face and her elbow resting on the windowsill. (00:18:50)
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.