There is internal logic, and there is good and bad reading, but the most important thing is whether something is convincing or not.
Someone used the words 'deus ex machina' a couple of pages back on this thread and they were good words to use.
It doesn't matter whether or not something is "correct" or "logically possible" or "congruent with the story" or whatever –*when you have a fiendish difficult, cliffhanger situation in which somebody is placed, it's always a bit of a let-down when they get out of it too easily, in a way that feels like a bit of a cop-out.
The thing about the deus ex machina in Greek theatre, or Shakespeare, or Joe Orton, is that it is employed either semi- or entirely self-consciously: it is something that draws attention to it's artificial status in order to highlight the theatricality, the "there but for the grace of God go I", the "it may be formally a happy ending, but we all know it's not really". It leaves a bad taste in the mouth.
The Dr Who endings don't recognise that. They just have a tendency to laziness: it's just a bit too easy.
Am I right or wrong in thinking that the old Dr Whos didn't really mess about with the paradoxes of time travel overmuch? I don't remember characters often going back over their own timelives at all, let alone the Dr. It was generally the Dr just using the Tardis to get from A-B, whatever period of history that was.