The Curse of the Black Spot - S6-E4
Visible crew/equipment: When Amy pulls out a sword before fighting the pirates, you can see a cameraman's reflection on the blade. (00:04:12)
Visible crew/equipment: When the Doctor is painting the fence and vacuuming the living room, Amy lifts her legs to let the Doctor pass with the vacuum, revealing the transmitter for her mic in her back pocket. (00:07:45)
The Bells of Saint John - S7-E8
Visible crew/equipment: When the Doctor and Clara are riding through London on their motorbike, the camera rig filming them is visible in their helmets. (00:29:05)
The Bells of Saint John - S7-E8
Visible crew/equipment: After Miss Kizlet enters her office to find the walking base station Doctor sitting at her desk, as she walks around the motorbike lying on the broken glass, when this 'Doctor' says, "Yes, those still with bodies to go home to would be free," we can see the moving reflection of two crew members on the surface of the motorbike.
The Bells of Saint John - S7-E8
Visible crew/equipment: When on the motorbike, the camera vehicle and equipment is reflected on the Doctor's helmet.
Visible crew/equipment: On the Moon's surface, the camera and boom mic can be seen reflected on the visor of the astronaut as she talks to Clara.
Visible crew/equipment: Just after Missy treads on Osgood's glasses after killing her, you can see a boom mike shadow on the wall.
Visible crew/equipment: When Bill and Nardole run away at the end of the countdown, the reflections of the camera dolly and camera operator are visible on the CERN countdown board. (00:35:55)
The Pyramid at the End of the World - S10-E8
Visible crew/equipment: Right before the TARDIS materializes in the lab at Agrofuel, there's an overhead shot of Erica at the desk, and the two green tape X marks on the floor behind her are visible, precisely where Douglas had collapsed and his white protective gear should be. Note there's an earlier overhead shot of the same area before the incident, when Erica brings Douglas the coffee, and those tape marks are not there. (00:32:50)
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.