I think possibly after re-reading the dialogue between the Architect and Neo that Neo had Matrix Code evolving into advanced stages as time progress. This would explain his increased abilities. When he was supposed to go through that door though to the core for dissmenation of the code inside of him, think about this. How could it read the code unless it had something to read though, kind of like a port through the back of the computer. That port inside Neo opened up, in preperation for dissemination of the code, but he doesn't go through through the door the core. His port is still open and he leaves through the door he came in. I think with the ability to harness the "prime program" that he carries now, he can do more things than he thought he could. Remember, the Prime Program is used to rebuild the Matrix. Neo is a walking, living, breathing source code and can manipulate it and program it to do anything he wants it to know. He just didn't know it.