Silence in the Library (1) - S4-E8
Revealing mistake: When the Doctor notices the unnatural triangular shadow signalling the presence of the Vashta Nerada and points it out to Donna, the shadow appears over Donna when she's standing in front of it, showing that it's a special effect added to the shot afterwards. (00:11:10)
Silence in the Library (1) - S4-E8
Revealing mistake: Also applying to the second episode of the two-parter, "Forest of the Dead": The keyboards on the Library's computer terminals are very obviously standard Apple keyboards - this in an episode set in the 52nd century.
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.