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)
Daleks in Manhattan (1) - S3-E4
Continuity mistake: When Diagoras enters the Daleks' lab, he is shown pulling on his right glove twice. (00:18:55)
Daleks in Manhattan (1) - S3-E4
Continuity mistake: When Frank is dragged off by the pig-slaves, the manhole opening into the theatre is depicted as completely open from below. When the shot switches above to the stockroom when Solomon pushes the Doctor away from the manhole, the lid is resting half over it, before it being completely open when Solomon moves to pull the lid over the manhole and close it. (00:23:14)
Daleks in Manhattan (1) - S3-E4
Continuity mistake: When the Doctor is taking the back off the radio, his grip on it changes between shots. (00:25:15)
Daleks in Manhattan (1) - S3-E4
Continuity mistake: When Tallulah is reunited with Laszlo, she puts her hands on his shoulders. Then, between shots, they jump to his neck, then the collar of his jumpsuit, then his jaw, etc. (00:39:35)
Daleks in Manhattan (1) - S3-E4
Continuity mistake: Near the end, when Martha asks the Daleks what's going on and one of them explains that they are planning to evolve to live outside their shells, the Doctor changes position between shots while he's shown listening to this, standing behind Frank and Laszlo. (00:44:30)
Daleks in Manhattan (1) - S3-E4
Continuity mistake: When Diagoras is seen being merged with Dalek Sec, he has gloves on, but when the hybrid Sec emerges, the gloves are gone. (00:45:00)
Daleks in Manhattan (1) - S3-E4
Plot hole: The guy working for the Daleks offers the homeless men in Hooverville a dollar a day to go into the sewer because the Daleks need more people. Most of the people refused and one called it slave wages. If they were not getting paid until they came back, and since the Daleks were planning on experimenting on them, the people weren't going to come back; why not offer them a large amount of money big enough to entice them but small enough not to be suspicious?
Evolution of the Daleks (2) - S3-E5
Continuity mistake: When the hybrid Dalek Sec declares that the human prisoners in the lab will become like him, the Doctor is shown ducking out of the group to the side of the lab twice, in two successive shots. (00:01:15)
Evolution of the Daleks (2) - S3-E5
Continuity mistake: When Dalek Sec tells the Doctor, "The Cult of Skaro escaped your slaughter," the Doctor is lowering his chin. In the next shot, facing the Doctor, as he asks Sec how they survived, he still has his chin raised and head tilted back. (00:01:55)
Evolution of the Daleks (2) - S3-E5
Revealing mistake: When Dalek Sec picks up the remains of the radio and turns it in his hands, the "Hamilton" label on the front of the radio is written backwards, indicating that the shot has been flipped horizontally. (00:05:00)
Evolution of the Daleks (2) - S3-E5
Audio problem: When the Dalek says "Humans will be spared", its ear lights are out of sync with the words. (00:11:40)
Evolution of the Daleks (2) - S3-E5
Continuity mistake: After the Doctor slips Martha the psychic paper, when he and the Daleks leave, Martha is shown bringing her hand close to her body and opening the wallet with the paper. In the close up, she repeats the two actions. (00:12:05)
Evolution of the Daleks (2) - S3-E5
Continuity mistake: When Martha is searching for how the Daleks changed the design of the Empire State Building, she is examining the plans for the top of the tower. In the first shot where the new plans are visible, the upper right shows a more detailed picture of a plate of Dalekanium. Seconds later, when we can see the new plans again, it's the same side view but the enlarged picture of the plate with the Dalek bumps is gone. These are still the same new plans (the old plans are on her right) and there was no time or reason for Martha to take another page. (00:24:40)
Evolution of the Daleks (2) - S3-E5
Revealing mistake: When the people in Hooverville are meeting around the campfire, it's raining. However, everyone's clothes and hats are completely dry. (00:28:05 - 00:28:45)
Evolution of the Daleks (2) - S3-E5
Visible crew/equipment: As the Daleks present Sec in chains on the theatre stage, a stagehand is briefly seen moving behind them.
Evolution of the Daleks (2) - S3-E5
Other mistake: After the hybrid Dalek Sec explains the Daleks' plan to harness the power of a solar flare to the Doctor, when the Doctor asks how many minutes until the flare arrives, Sec says it's in 11 minutes. A fair amount of action and backstabbing later, when the Doctor and Laszlo arrive at the top floor of the Empire State Building and after the Daleks take back control of the elevator, the Doctor says that the solar flare arrives in 6 minutes. It is a considerable stretch for everything that happens between those two moments to take place in only five minutes.
The Lazarus Experiment - S3-E6
Continuity mistake: When the Doctor is saying goodbye to Martha, he's leaning on the open TARDIS door with his hand open. When Martha says that things just kind of escalated, the Doctor's hand is suddenly a fist. (00:02:00)
The Lazarus Experiment - S3-E6
Continuity mistake: When Martha compares the Doctor's tuxedo to James Bond, he's adjusting the bowtie. The position of his hand changes between the wide shot and the close-up as he responds, "James Bond? Really." (00:04:25)
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.