Continuity mistake: The cables on the window washer's bucket are fine until Foster shines her sonic pen on it. In the close up, the spot on the cables looks to be already cut and of course wired with the pyrotechnic device. (00:26:15)
Continuity mistake: When Miss Foster uses her sonic device on the window-washer's crane, she points it at the right-side cable, but it's the left-side cable that breaks. (00:26:25)
Continuity mistake: When Ms. Foster's computer switches back on because it's picking up a signal from the Adiposian First Family, in a shot facing him, the Doctor reaches towards it with his left hand. In the next shot, from behind him and Donna, his left hand is resting on the wall next to the computer, before he reaches for it again. (00:39:25)
Continuity mistake: When the Doctor attempts to persuade Matron Cofelia, who is hanging in a levitation beam, to come over to the roof of the Adipose Industries building, Donna's hands, resting on the parapet on the edge of the roof, change position between shots. (00:41:15)
Continuity mistake: Just before Penny Carter tells the Doctor and Donna that she's going to report them for "madness", the Doctor is seen holding Miss Foster's sonic pen, which he threw in the trash just moments earlier. (00:42:10)
Continuity mistake: At the end of the episode, Donna piles suitcases in the Doctor's arms in preparation to leave with him in the TARDIS, and places a striped hat box on top. The bags stay that way for a while as the camera cuts back and forth between them, and you can see the stack of luggage as the camera films the Doctor from behind. Then, as soon as the camera cuts back to the Doctor's face when Donna leaves to give her mother the car keys, suddenly he has one bag under his arm and another in his hand, and the rest of the bags are on the ground with the hat box stacked neatly on top. In addition, when the scene cuts from Donna closing the hatch of her car to her and the Doctor standing by the TARDIS, a large floral-patterned suitcase has appeared, which she was not shown removing from the vehicle. (00:43:15)
Other mistake: Near the start, the Doctor and companion, just after having experienced a violent earthquake within the city of ancient Pompeii, discover someone sold the TARDIS after fleeing toward where they parked it and finding it gone. But where it had stood there is a floor to ceiling shelf of clay pots, very aligned, unshaken, unmoved from the shelves. (00:04:00)
Continuity mistake: When the Doctor and Donna are talking to Caecilius, when they introduce themselves as "Spartacus" and Caecilius makes several guesses as to their relationship, wondering if they're married or siblings, in shots facing them, the Doctor and Donna are standing fairly close together. In shots facing Caecilius, however, the Doctor and Donna are standing much further apart. (00:11:05)
Continuity mistake: After Lucius' arrival, when the Doctor escorts Donna towards the TARDIS, telling her they have to go, which she doesn't agree with, between shots his hands change position between having his right hand on her back, or having both his hands on her shoulders. (00:13:55)
Continuity mistake: When the Doctor and Caecilius are talking while the Doctor examines the hypocaust, Caecilius keeps changing position. (00:17:40)
Continuity mistake: In Lucius' house, when the Doctor pulls the cloth off the shelf with the stone circuits, the position of Quintus' hand on the shaft of the torch he's holding changes between shots. (00:19:10)
Continuity mistake: When Donna changes into contemporary clothing, she has a purple shawl of sorts draped over her dress. In the first shot, she's shown with her hand out from under the cloth, but in the next shot her hand is under the cloth. (00:19:30)
Continuity mistake: When the Sybilline priestesses kneel after the High Priestess speaks, in a shot from the front, Donna, sitting on the altar, has her hands in front of her - she's using her left hand to take the rope off her right wrist. In the next shot, from behind, her hands are at her sides. In addition, the rope still on her right wrist disappears. (00:27:05)
Revealing mistake: When the Doctor and Donna are walking through the underground tunnels towards Mount Vesuvius, tunnels that can be presumed to be fairly warm due to their connections to volcanic activity, their breath is visible - something that only happens in cold temperatures. (00:31:20)
Continuity mistake: When the Doctor explains to Donna how he sees the universe, the distance between them changes several times. (00:31:40)
Plot hole: After getting out of the Pyrovile escape pod, the Doctor and Donna start running back to Pompeii. In the process, they are somehow able to outrun what appears to be a pyroclastic flow. Pyroclastic flows can reach speeds of up to 700 kph, and should be impossible for them to outrun. (00:38:15)
Continuity mistake: When the Doctor is talking to Evelina at the end, her hair changes position between shots. (00:44:00)
Continuity mistake: When the Doctor and Donna leave as Caecilius, Metella, Evelina and Quintus stand and watch the destruction of Pompeii, the TARDIS changes orientation between shots - in both of them, one from in front of the family and one from behind, the TARDIS' door, with the sign, is visible. (00:45:10)
Continuity mistake: After Metella hands Caecilius the beetle brooch, his hands change position between the close-up and the wide shot. (00:46:10)
Continuity mistake: For most of the scene where the Doctor and Donna find the dying Ood Delta-50, the front of his body is covered in snow. After he mentions "the circle", when the Doctor is asking what that is, the snow on Delta-50's chest is gone. In addition, the Doctor's hands change position between shots. (00:06:25)
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.