What happen in episode 13.5?
The so-called "episode 13.5," titled "Another Epilogue" was released as an extra on the BD/DVD exclusive. Depicted is an short alternate ending where Otonashi remains in the school and becomes the new student council president, in order to help other students (like how Tenshi did) to pass on. It's really a "what-if" scenario rather than an actual epilogue.