The Sontaran Stratagem (1) - S4-E4
Visible crew/equipment: As the Doctor tries to get Wilfred out of the car, the camera goes to follow his movement and there is a reflection of the lighting rig and camera on the car.
Continuity mistake: When the Doctor pulls out a TARDIS key to give to Donna, the exact position of the key in his hand changes between shots. (00:05:00)
Factual error: Colonel Mace says the Sontaran ship is orbiting 5,000 miles (8,050 km) above the Earth. However, in shots of and from the ship in both this episode and "The Sontaran Stratagem", the Earth appears far too small for the ship to be that close, with the ship's true distance appearing to be well over double that. (00:08:34)
Other mistake: When the Earth's nuclear launch sites are being brought online, country by country, in preparation for a strike at the Sontaran ship, Russia is puzzlingly omitted, even though North Korea of all nations is included. (00:17:20)
Visible crew/equipment: During the warehouse battle, around when the Doctor tells Donna, "Hold on, I'm coming", the film crew can be seen reflected in a door at the right of screen. (00:28:20)
Continuity mistake: When Colonel Mace confronts Commander Skorr, he raises his gun twice; once in one shot, and immediately after in the other. (00:30:30)
Continuity mistake: When the Doctor activates the teleport, Donna is onboard the Sontaran ship, holding a cell phone in her left hand. When she arrives in the basement of the ATMOS factory, she's holding the rubber mallet in her left hand, and her right hand is empty, with the phone nowhere to be seen. (00:32:40)
Continuity mistake: Near the end, when Luke teleports and switches places with the Doctor on the Sontaran ship, Luke catches the atmospheric converter's switch twice, once in the wide shot and then again in his POV. (00:40:25)
Continuity mistake: When Donna is sneaking around the Sontaran ship, she's carrying Martha's old phone, which she's using to stay in touch with the Doctor, and the rubber mallet from the TARDIS. There are times when one of the two objects, the phone more often, is missing from her hands with no explanation.
Continuity mistake: When they get out of the TARDIS at the beginning, Martha and Donna change positions relative to each other between shots. (00:00:55)
Continuity mistake: During the conversation where Donna gives Jenny her name, Jenny's ponytail keeps changing position between draped over her shoulder and hanging in the back. (00:06:55)
Continuity mistake: In the scene where Cobb is briefing his troops, the troops all have their guns, but in the other scene (after you see the Hath marching) the troops are receiving guns. (00:15:45)
Continuity mistake: When Donna suggests that she distract the next guard using her "womanly wiles", she flips her hair behind her shoulder. In the next shot, when the Doctor tells her to save her wiles for later, the hair has spontaneously moved to its former position. (00:19:35)
Continuity mistake: When the Doctor starts scanning the wall of the tunnel as Jenny asks him who he is and if he's an anomaly as well, his grip on the sonic screwdriver changes between shots. (00:22:20)
Continuity mistake: After the Doctor opens the secret door in the tunnel wall, he puts the sonic screwdriver into his inner jacket pocket. In the next shot he's in, as he says, "Now, what were you saying about running?", he does it again. (00:22:55)
Other mistake: Martha falls into the bog and Hath Peck rushes down to help her. She calls out "Help me, Peck!" but the subtitles read "Help me peg!" This is just one of many errors in this series' subtitles, which seem to have been added by listening to the dialogue without reference to the script. (00:26:30)
Other mistake: When Jenny does somersaults through the laser beams, the last two beams are level horizontally and the higher beam is lower than her foot, so she should have broken it.
The Unicorn and the Wasp - S4-E7
Continuity mistake: When Robina Redmond is announced, and Lady Eddison says, "She's the absolute hit of the social scene - a must," in the first shot, Lady Eddison is standing close enough to her wheelchair-bound husband to cast a shadow on him. In the second shot, the distance between them has suddenly increased. (00:05:10)
The Unicorn and the Wasp - S4-E7
Continuity mistake: After questioning the houseguests, the Doctor and Agatha are talking. She uses the phrase "little grey cells", and the Doctor responds, "Oh, yes, little grey cells. Good old Poirot." When he does this, he's holding a saucer in his left hand and rests a teacup he's holding in his right hand atop it, as he turns toward the chair that the suspects were sitting in. In the next shot, as he walks over and sits in the chair, he is suddenly holding the teacup and saucer in his right hand, with his left hand in his pocket. (00:13:55)
The Unicorn and the Wasp - S4-E7
Continuity mistake: After the Doctor opens the Unicorn's case of tools, his right hand changes position when Greaves enters the room to deliver drinks. (00:22:20)
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.