Continuity mistake: When the Doctor asks Captain McDonnell how many other crewmembers there are on board, he grabs her arms. After she tells him "three", the Doctor lets go of her as Scannell explains that the ship transports cargo across the galaxy. In the next shot, facing the Doctor, he's holding McDonnell's arms again. (00:03:00)
Continuity mistake: When the Doctor starts scanning Korwin, he's holding the sonic screwdriver with his thumb on the end without the light. When Ashton says that Korwin sabotaged the ship, the Doctor's grip on the screwdriver has changed to one without his thumb on the end. Shortly after, he has his thumb on the end again. (00:06:10)
Continuity mistake: When the Doctor comes up with the idea of using the generator to restart the ship's engines, in a close-up he's gesturing with his right hand, but in a wide shot is gesturing with his left. (00:10:15)
Continuity mistake: After McDonnell warns the crew that the possessed Korwin killed Abi, Ashton orders Erina to hurry up with the equipment she was sent to fetch, and she mutes the com before removing several pieces of equipment from a locker, holding them with her right hand and arm. When she closes the locker door, revealing Korwin, the equipment disappears. (00:15:20)
The Lazarus Experiment - S3-E6
Continuity mistake: After Lazarus switches his machine on while the Doctor and Martha are inside, when Martha asks what's happening, the Doctor, who is working on the machine, is holding several coloured wires, most prominently white and blue, in his left hand and has a white wire wrapped around his right hand. The scene cuts to Martha, and when it cuts back to the Doctor, the wire around his right hand is gone and he's only holding a white wire in his left hand. (00:29:10)
The Lazarus Experiment - S3-E6
Continuity mistake: When the Doctor and Martha get into Lazarus' machine, it's shown to be very cramped inside - when the Doctor crouches down to access the wiring and circuitry below a floor panel, his head is right next to the skirt of Martha's dress. However, after he tells Martha what he's doing to the capsule, when he notes that the transformed Lazarus is three times the size of his human form, the Doctor is further away from Martha. (00:29:25)
The Lazarus Experiment - S3-E6
Continuity mistake: After the Doctor and Martha get out of the capsule and walk up to the human Lazarus, lying on the floor, Martha says it's kind of pitiful, turning to look at the Doctor as she does so. In the next shot, facing the Doctor, Martha's head is still turned to look at Lazarus. (00:30:10)
The Lazarus Experiment - S3-E6
Continuity mistake: In the cathedral, when Lazarus says, "You're so sentimental, Doctor. Maybe you are older than you look," his blanket has jumped up to cover his left shoulder, which was previously bare. The blanket then changes position several more times. (00:34:50)
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)
The Lazarus Experiment - S3-E6
Continuity mistake: After Martha hugs her mother, when Francine asks what the occasion is and Martha responds that she's just pleased to see her, in a shot facing Francine she has her right hand on the side of Martha's head. In the next shot, facing Martha, Francine is moving her hand to the position it was in the previous shot. (00:06:15)
The Lazarus Experiment - S3-E6
Continuity mistake: When Lazarus starts his speech, there is a shot of the Doctor and Martha watching. The Doctor has his arms at his sides. The scene cuts to Lazarus speaking, a shot in which the Doctor is visible from behind, unmoving. In the next shot of the Doctor, he has his arms crossed. (00:07:15)
The Lazarus Experiment - S3-E6
Continuity mistake: After Lazarus emerges from the pod, when he announces himself to the crowd, in a wide shot, his arms are lowered, but in a close-up immediately afterwards his arms are raised. (00:09:15)
The Lazarus Experiment - S3-E6
Continuity mistake: During the reception, the newly rejuvenated Lazarus takes a tray of hors d'oeuvres from a waiter and starts eating them while talking to Lady Thaw, just as the Doctor and Martha walk up. Later in the conversation, just as Lazarus says to the Doctor that what happened inside the capsule was exactly what was supposed to, the tray vanishes. (00:11:10)
The Lazarus Experiment - S3-E6
Continuity mistake: When Lazarus begins transforming into the giant scorpion monster the first time, he's holding a tumbler of alcohol. When he drops to the floor as Lady Thaw asks what's wrong, the glass has vanished. (00:15:20)
The Lazarus Experiment - S3-E6
Continuity mistake: When Francine calls Tish over to ask her if she's seen Martha and the Doctor anywhere, Leo is taking a drink from a nearly-empty glass of champagne. When Leo is next seen on camera, as Francine asks Tish if Martha had ever mentioned the Doctor to her before, he's drinking from a much fuller glass of champagne. (00:16:00)
The Lazarus Experiment - S3-E6
Continuity mistake: When the Doctor and Martha enter Lazarus' office, as the Doctor wonders where Lazarus is, in a wide shot he puts his hands in his pockets. In a close-up immediately afterwards, his hands are by his sides. (00:17:00)
Continuity mistake: When the Doctor fits the Chameleon Arch watch into the headset, his hands change position between shots. (00:20:15)
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)
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)
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.