Continuity mistake: When the Doctor puts on a harness during the preparations to rescue Hila, a flap on the front keeps switching between being straight out and being folded behind the strap it's attached to. (00:29:25)
Continuity mistake: When Clara shakes the TARDIS' doors, demanding it let her in, her hands change position between shots. (00:36:25)
Continuity mistake: While Emma is explaining to Clara what an empathic psychic is, the Doctor grabs a bottle of milk from the table and takes a swig out of it, holding the bottle in his right hand, before jumping into the conversation to state that empaths are both extremely compassionate and extremely lonely. While he's saying this, his left hand goes from gesturing in a close-up to holding the milk bottle in a wide shot. (00:06:25)
Continuity mistake: When Emma tells Clara not to trust the Doctor, the position of her hands and fingers, holding her teacup, change between shots. (00:19:00)
Continuity mistake: When Clara draws the Doctor's attention to the vision of a forest appearing in the archway, the candelabra she is holding has two candles in it, with the third hole empty. Moments later, after the apparition has disappeared, there are now three candles in it. (00:15:30)
Continuity mistake: For most of the episode, there is a thunderstorm going on at Caliburn House. However, when the TARDIS is seen dematerializing and rematerializing when the Doctor and Clara go to take pictures of the ghost throughout time, it's dry in the grove where it was parked. The first time is especially noticeable, as moments later we are shown Professor Palmer and Emma looking through a rain-spattered window, commenting on the noise of the TARDIS' engines.
Factual error: The Doctor says that the Earth is six billion years old, which is one and a half billion years over - it's only 4.5 billion years old. (00:21:25)
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.