Steven Moffat and the BBC are being very tight lipped on the 50th Anniversary specials. I know of 3 so far; the special 50th Anniversary episode, The Day of the doctor, the docudrama, An Adventure in Space and Time, and a documentary. Unfortunately I can't quite understand why they are being so secretive about the later two. The special episode makes sense, it would be hard to show much without giving too much away. However, they aired a trailer for it at Comic-Con this summer, so there are a few people out there who know more than the rest of us. The docudrama, An Adventure in Space and Time, was also previewed at Comic-Con, it has no connection to the story of the 50th Anniversary episodes, and as of yet, no date or time has been announced and the trailer (viewable as a very bad cell phone video) remains unreleased. I would think they would want to build interest in that.
Then there are the hints and rumors. There are lots of rumors, few should be headed in any way. The only things I've been paying attention to are Steven Moffat's posts on Facebook. One of them was delightfully intriguing about John Hurt's Doctor without actually revealing anything. Hurt's Doctor is definitely earlier in the Doctor's timeline, but so far nothing official from Moffat about when. There are delightful hints of the Time War or maybe something much earlier, but nothing definite.
But there is one possibility that has occurred to me that allows for John Hurt's Doctor without changing our familiar sequence of Doctors. In the Time War things changed. Who knows what alternate timelines might have happened. It is seeming more likely that John Hurt's Doctor is the 9th Doctor, but not from the main timestream we are following. I see two possibilities; that he is from an alternate timeline that was erased/sealed by the end of the Time War, or that he is the same incarnation as Eccleston, but something happened to rejuvenate him without regeneration. In either case, I think, if all the theories about the Time War prove to be correct, that Hurt's Doctor is the one who ended the Time War and destroyed Gallifrey and the Daleks. That is monumental enough for the shame heaped upon him. Still, this is all just speculation and the only source that Hurt's Doctor comes between 8 and 9 isn't from a reliable source for the plot. The pieces do seem to fit together, but we will see.
With the regenerations we've seen in the series, the only places Hurt's Doctor could fall (if he is a separate incarnation and not some variant of one of the others or from and alternate timeline) is before Hartnell, between Troughton and Pertwee, or between McGann and Eccleston. All the other regenerations have been seen on screen and even the Troughton to Pertween regeneration was implied, thought not actually shown (Pertwee exits the Tardis in Troughton's clothes).
And Hurt's Doctor being from the Time War does have one strong bit in its favor. Clara went all through the Doctor's timeline and didn't see Hurt's Doctor. The Time War was locked so nothing could escape and nothing could get back in. That would likely apply to routing through the Doctor's own timestream so Clara would not have seen any of the Time War and not seen Hurt's Doctor. But then, how do we get to see him in this special? The more ideas pop up, the more questions there are to answer. But we are now less than a month from the 50th Anniversary and that much closer to seeing the episode and knowing. Until we get better clues or get to see the episode itself, it is all just speculation. Don't get your hopes up on any of these guesses. Keep your mind open so you can enjoy it as it unfolds.