I'll explain later...

TV Doctor Who is namechecked in this excellent article about internal continuity within franchise universes. The general message seems to be -- we have it very easy indeed:

"The British sci-fi TV series Doctor Who, judging by the official series chronology book, 'A History of the Universe', has taken a more relaxed approach to continuity matters, making no effort to reconcile contradictions (such as three unrelated explanations for the sinking of Atlantis) even when the errors could be rationalized with ease (as, for instance, when one of the Doctor’s time-traveling companions says she is from 1980 but is later depicted as a native of the 1970s, implying that an organization she works with may have been disbanded even before it was founded—if we stubbornly refuse to posit that she was rounding off when she said “1980,” that is)."

Not wanting to get into UNIT dating, the way I've always rationalised the Whoniverse (is that a word?) is that the web of time is in a constant state of flux, that The Doctor might turn up somewhere at roughly the same time on a number of different occasions and it might appear changed because of something he or another time traveller has done earlier. So there can be multiple reasons the Marie Celeste has sunk. Of course all kinds of other unmentionables (like does Rose remember seeing Mondas in the sky in '86?) can be explained away by the introduction of selective memory that we saw in World War Three. Now about him being half human ... [via]