I just read through a lot of pages of comments. I'm going to try to contribute.
1) In the Tower of Joy scene Lyana clearly says "His name is Aerys." She's saying that Jon Snow's name is really Aerys, after his grandfather, the mad king.
2) While Jon and Sansa are not brother and sister, they are cousins and they have lived their whole lives as brother and sister. Anyone who envisions some kind of romantic scenario between them is crazy.
3) Jon might be a bastard but who cares at this point? He IS the King in North and the entire Northern power, plus the Aerie is behind him. He legitimizes himself.
4) Related to #2, Sansa is never going to marry again unless it is completely on her terms. She will never allow someone else to have power over her.
5) Dany is going to marry someone. It will be a political marriage, not one for love. She and Jon make perfect sense. He wants to stop the undead, she will help make that happen.
6) Tyrion is not married to Sansa. They did not consummate that marriage. Also, Tyrion will never love another. Much the same way that Sansa has been damaged emotional, so has Tyrion by Tywin.
7) I don't believe Sansa knew exactly when the KoV were coming. She was urging Jon to wait but she didn't know for how long. Yes, television has horrible coincidences.
8) There is no conflict with Sansa and Jon. Look at how happy she is for him when they are proclaiming him King in the North. LF might try but she is not dumb Sansa anymore. She is much more cunning. Look at the way she rebuffed LF in the Godswood. She never told him no and she was gentle. She even said something about how it is a nice picture he has in his head.
9) Tyrion was an amazing Hand of the King.
10) Why would Dany land in Dorne and then slog up the continent? There's only one place she is landing and that is Dragonstone. Followed shortly after by King's Landing.
11) There is no Cersei's alliance. She has run out of time. She is the ruler of nothing except the Western Heartlands, maybe the Storm Lands, the Riverlands and King's Landing. All of that means very little when it comes to armies. Cersei's problem is that she has always had Tywin's ruthlessness without his long term strategic vision.
12) No way Littlefinger can leave. He declared for the Starks.
13) I think we can firmly put away all the various Arya theories. There is no reason for her to declare, to an empty room and Walder Frey, that she is Arya Stark. Look for Arya to have somehow attached herself to Jaime's camp and make her way to KL.