Father's Day - S1-E8
Plot hole: In "Aliens of London", it is established on a 'missing person' poster that Rose Tyler is approximately 19 years of age in March 2005 (The poster says 'missing since 6 March 2005'). This means that she must have been born prior to March 1986. However, in "Father's Day", which is dated 7 November 1987, Rose is still a baby in her mother's arms, when she should be a toddler aged approx two.
Father's Day - S1-E8
Continuity mistake: When Rose checks her messages while riding in Pete's car and hears the very first phone call instead, the positions of her fingers change between the wider shot and the close-up. (00:13:30)
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.