13 hxg6 is a bad situation for black, so good job on that. Taking the pawn though is a mistake for 14. Bxg6! ... fxg6 15. Qxg6 checkmate. The opponent wanted to relieve pressure on the h7 square, thus h5.
Meanwhile, I do not recommend 16.Bxf6. It's not a mistake, it's not even a bad move, but just thinking about the endgame, bishops are stronger than knights. I wouldn't done 16. Ne5 which would lead to ... Rg7 17. Ng7 ... Nxg7 18. Bxg7 and then take the h pawn and start hammering into that rank.
Those are some of the real things I saw about this game. Everything afterward is all because of that little computer error with that misplaced rook. Everything else in the endgame played out nicely, if anything you can find some moves that were less accurate then others, but not significant game changing events. I really like the Queen sacrifice though. It's stylish. :)
I gave some very brief 'analysis' but I can't really analyze my own games, so any insight is much appreciated.