The Bells of Saint John - S7-E8
Factual error: Clara determines the location of the enemy's base of operations: floor 65 of The Shard. However, there are multiple issues with this conclusion. Firstly, floor 65 is a residential property, not an office location; offices in The Shard occupy floors 2 through 28. Secondly, the view of 30 St Mary Axe from Miss Kizlet's window puts the office below 180m, the height of the latter building. This would mean the office must be below floor 50. Finally, when the Doctor rides his motorcycle up the side of the building, 30 St Mary Axe is again seen, this time significantly below his location, and on the wrong side of The Shard. Not only then does the office's height change, but also which side of The Shard it is on. (00:36:06 - 00:38:40)
The Bells of Saint John - S7-E8
Factual error: The view from Ms Kizlet's window was taken somewhere in the vicinity of London Wall eg. the Museum of London, not from The Shard.
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.