Factual error: Magnetic tape recorders weren't available outside of Germany during World War II. True the tape recorder could have been captured from the Germans, but, as it was "cutting edge" technology for 1941, it would hardly be likely to have ended up in a hospital office.
Revealing mistake: Dalek is escaping and enters the large room with the soldiers. He starts the sprinklers so he can kill them faster. When they show the dead soldiers they show some casings which were ejected from the soldiers' guns. The casings still have projectiles in them. If used, they would have been in magazines and would never fall out like they are shown.
Doctor: So, that's the trap. Or the test or the final judgment, I don't know. But if I kill you, I kill her. Except that implies, in this big grand scheme of Gods and Devils, that she's just a victim. But I've seen a lot of this universe. I've seen fake gods and bad gods and demi-gods and would-be gods - out of all that - out of that whole pantheon - if I believe in one thing... Just one thing... I believe in her.
Doctor: Pfft... I'd have to settle down. In a house or something, a proper house with... With... With... With doors and things. Carpets! Me! Living in a house! Now that... That is terrifying.
Rose: You'd have to get a mortgage.
Rose: Oh yes.
Doctor: I am dying. That's it. I am dying, it is all over.
Answer: The Master knows that deep down, he deserves death for the crimes that he's committed throughout his life, and since he regards The Doctor as his arch-foe, he expects it to be at his hands. The fact that The Doctor is still willing to forgive him for all of his crimes hurts him more deeply than death would.
Question: Is there any information on the entity shown in "Midnight?" It seems interesting enough to have some depth to it. It seemed to be bad in nature. It also seems to have been exactly what the woman that was possessed was afraid of.
Answer: No, no information is avalible for the identity of the entity.
Question: 1. Why was Rose not allowed to touch her past self without creating a paradox and causing those creatures to appear and eat everyone, but Amy was allowed to touch her younger self without any repercussions? 2. Why was Rose able to have the time vortex in her head for a few minutes and it only knocked her unconscious whereas the Doctor had it inside him for about 30 seconds and it basically killed him and caused his regeneration?
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.