2. Time Stream Corruption/Temporal Collision
At the end of The Name of The Doctor, The Great Intelligence, Clara and Eleven all enter The Doctor's time stream. The Great Intelligence is spread throughout and causes chaos and destruction. And Clara is spread out to put right what once went wrong. But Eleven seems to end up at the center of his time stream with all of his past and future versions. Here, he rescues Clara and confronts John Hurt's Doctor. There was so much emphasis put on The Doctor never going to Trenzalore since it was first mentioned in Series 6. In the Series 7B finale, The Doctor says that it is the most dangerous place in the universe and he begins to get sick just being near his time stream. The paradox is too much. What if, by entering the time stream, The Doctor caused major ripples through time and space? Perhaps, he broke time. Different time periods are melding causing Ten and Eleven run into one another. Meddling with his time stream have cause a temporal collision like in the 2007 minisode Time Crash.
Likelihood to Happen: 5/10 - As much as I like this theory, I feel like it is only a partial explanation for the events of the 50th anniversary special. I mean, there has to be consequences for entering your own time stream, right?