1. Everything -- telly, books, audios, comics, lolly sticks -- is true.
1a. Especially the bits that seem to contradict each other.
1b. Especially especially the bits that were deliberately written to contradict each other.
1c. It's also particularly true of Gallifrey canon. Apparent contradictions are just a sign of higher truths (hey, the whole "it's a mystery" thing works for RL religions).
2. Fitz could never leave, because when the TARDIS reconstructed him in Interference, it had to fill in his motivation and it could never believe anyone might want to leave the Doctor.
2a. Trix ended up leaving him over this, but they had a lot of fun along the way.
2b. His inability to leave led to Fitz's death in the closing stages of the War, Nine wearing his jacket, etc. (Everyone has some variant of this on their list, I think.)
3. Those cows in the final pages of The Flood, when Eight and Destrii are walking off into the sunset? Are the Skrulls that Reed Richards hypnotised into being cows that one time. (Hey, it's all Marvel. Just about.)
4. The Doctor (in general, not just Ten, though this is a particularly strong trait in his personality shuffle) is congenitally incapable of expressing his feelings to people. He thinks actions speak louder than words and so ignores the words side of things completely.
4a. Ten's ideal companion would be Bridget Jones, 'cos she would call him on his commitment-phobic emotional-fuckwittery.
5. "Song for Ten" exists in the Whoniverse, and was written by Whoniverse-Neil-Hannon after meeting him.
6. I believe there is plenty of evidence for the following ships in canon, let alone fanon: Ian/Barbara. Ben/Polly. Two/Jamie. Four/Romana. Nyssa/Tegan. Five/Turlough. Ace/every female guest star under 60 (and some of the ones over). Eight/Charley. Fitz/Anji. Rose/Mickey.
6a. Mickey/Jake. But they get a subclause all to themselves because there are lots of details in relation to this one.
6b. They never talk about the Rickey thing.
6c. That bit in The Beach Scene where Rose is disavowing the Doctor's assumption that she and Mickey are having a baby is more about the fact that Mickey and Jake are together now than the fact it's her Mum and Pete's baby.
7. And still on The Beach Scene, Rose was already well on the way to getting over it all when that whole weird telepathic dream happened, thank you very much, so really it was a bit fuckwittish of the Doctor to dredge it all up again and then not even say I love you (q.v. 4).
8. At the Fall of Arcadia, the Daleks used massed armies of clones of the Doctor's former companions as soldiers deliberately to break his spirit.
9. There are no connections between all the various people called "Jones", except for the fact that Martha's family are Martha's family. Honest.
10. The fact that the Doctor apparently loves Earth and humans so much is entirely an artefact of the fact that that's the planet we're watching his stories on. All those gaps in his timeline are filled with him travelling the universe with members of other species and saving their planets.
(Some of those are things that I came up with in the process of writing fic, which makes me feel a bit like a wanker, tbh. In particular, #8 is basically the premise of a fic I can't make work.)