There one major plot point that seems to be over looked. With the intro of John Hurt as a incarnation of the Doctor then Chris, David and Matt should be renamed the 10th, 11th and 12th Doctors. Just calling him the war doctor is a little bit of a cop out.
My stepfather and I have had this debate too, but the way it worked out is that once the War Doctor and Doctor Ten left, their entire memories of the event would be "restored" to think that Gallifrey had burnt, the Time Lords and the Daleks wiping each other out - though not really, in the case of the Daleks - to maintain the timeline and all that jazz. Only Eleven would know what had really happened (and Twelve after him, presumably), but all the prior incarnations would have the memories of the War Doctor being "best forgotten", with Eccleston remaining Nine, Tennant still Ten, so on.
I've actually heard the War Doctor referred to as "The Eight-and-a-Halfth Doctor" because he's sorta crammed between Eight and Nine; another example of "a Doctor who's not really 'the' Doctor", an in-betweener, is the Valeyard (Trial of a Time Lord, the four-part bit from Colin Baker's era), who is revealed to be the dark side of the Doctor given form somewhere between his twelfth and thirteenth incarnations.
