Okay, so. We have a one-word hint from Matt Smith: 'Paintings.'
And in a photo of David Tennant, a letter from Queen Elizabeth I can be seen, with the text 'until such time a a National Gallery is established'. So, the paintings are a pretty big deal.
Now, one of the biggest problems with a multi-Doctor story is the aging of the actors. Moffat was able to wing it with Time Crash, but that can't be repeated. So how could former Doctors be included in a 50th Anniversary episode?
Maybe there is a sequence of dimensionally transcendental paintings out there, each one representing the Doctor in one of his incarnations. They would be rendered using CGI, and as the episode is going to be in 3D, the audience could look right into them. And they could, Hogwarts-style, be able to speak and act.
This would allow previous Doctors to VOICE their parts, while neatly sidestepping the problem of actor aging. It would also, crucially, allow the actors to record their parts from wherever they happened to be in the world. So, for example, the fact of three of the Doctors being in New Zealand right now wouldn't necessarily be a problem. Previous Doctors could, if necessary, miss the read-through and the live-action filming, and be brought in later on for the CGI portraits.
Furthermore, one might say that an actor who is only voicing a part isn't technically appearing in the 50th Anniversary. Which neatly allows the various actors to keep the fans guessing - and on the edge of our seats with worry about whether or not we'll see any of them.
I have no idea what the plot might be, but we do know that Zygons are involved. Zygons are masters of imitation, so maybe the Zygons are trying to get hold of the Doctors' portraits, in order to perfectly mimic the Doctors and cause havoc throughout the universe?
As ever, it's only a theory. But it's a theory I will be clinging to in stark, pitiful desperation.