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)
Visible crew/equipment: After the acting Prime Minister gives orders to the sergeant and the lift doors close, the soldier turns around. As he issues orders, the boom mic is reflected on his goggles. (00:05:25)
Rise of the Cybermen (1) - S2-E8
Visible crew/equipment: Everytime we see a close up of Mickey's grandmother's face, we can see the crew and camera reflected in her glasses. (00:22:20)
Visible crew/equipment: When Rose and the Doctor are riding after landing, you see the camera, crew and lighting equipment reflected in their glasses. (00:04:00)
Visible crew/equipment: When Rose runs and hugs her mother, near the end of the episode, at the back wheel of the jeep, you can see someone's foot going down and then back up. (00:44:50)
Visible crew/equipment: As the black suited figure stops to look at Martha, the crew and equipment are reflected in the helmet and visor. (00:02:30)
Visible crew/equipment: When the Doctor is being held by the slab in the MRI room, there are some shots where what appears to be a lighting screen is reflected in its helmet. (00:29:55)
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.
Visible crew/equipment: As Sally enters the living room in the abandoned house, in the shot where she walks through the doorway, a cameraman holding the camera can be seen reflected in the window of the door next to her. (00:00:35)
Visible crew/equipment: As the Doctor tries to get Donna to jump to the TARDIS, as the camera is in a close up on her in the taxi, the yellow camera vehicle is reflected on the cab's paint. (00:12:50)
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.
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)
Silence in the Library (1) - S4-E8
Visible crew/equipment: While the Doctor tries to get into the data core (after Proper Dave tried) it cuts to the telephone still ringing, and when the young girl asks her dad why he's not answering the phone, just as he tells her that the phone is not ringing the boom mic dips into view at the top of the screen. (00:19:40)
Forest of the Dead (2) - S4-E9
Visible crew/equipment: When River punches the Doctor, laying him out, just as he drops to the floor we can see the actor's green tape mark at River's feet. (00:33:20)
Visible crew/equipment: When the Cyber-arm is shooting at the Doctor and Amy, there is a brief shot when the Doctor is talking where you can see the crew member who is shooting at them.
Visible crew/equipment: When Amy is guesstimating Amelia's age, the camera pans to the right and into a crew member's arm. (00:13:49)
The Impossible Astronaut - S6-E2
Visible crew/equipment: Just after Amy comes out of the bathroom, a boom mic can be seen popping up behind the agent's shoulder. (00:28:55)
The Impossible Astronaut - S6-E2
Visible crew/equipment: The astronaut coming out of the lake is twice in series 6: In episode 1, "The Impossible Astronaut", and in episode 13, "The Wedding of River Song." In "The Wedding of River Song", when the helmet of the suit is lifted the astronaut is revealed to be River Song. However, in "The Impossible Astronaut", when the helmet was lifted, a man's beard can be seen. Clearly the use of a double to avoid giving the reveal away too early.
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.