How to continue someone else's story gracefully, with fan-fiction?

I've been juggling some ideas for NaNoWriMo and one of them is a Doctor Who story. Now I've not read a great deal of fan fiction but I've never read any that I'd say that compares to the original, and often I feel most fan fiction is a written exercise in Misery, with the fan fic author directing the characters, plot and theme over to their (often wildly different) point of view. Reading these back feels unnatural and clunky, as though the very act of trying to continue someone else's story ruin's your own.

How can I avoid the pitfalls of writing fan-fiction? Or should I avoid it entirely?

Edit:

For the purpose of this question 'dangerous' means that it will naturally lead to the things I mentioned above: characters becoming Mary Sue's, and plot veering wildly from the original theme, as the author forces the plot to work their way. In short is it possible to continue someone else's story gracefully?