beginnerpost mortem (I finally won one!)

Hi, your opponent played a dubious opening starting with the move 2... Nf6. Usually, 2... e6 or 2... c6 are played. You did not take advantage of it, but here are two links on how to get an advantage against the bad, so-called Marshall Defense to the Queen's Gambit.
http://www.youtube.com/watch?v=6U5hKR-TXH8
http://www.chesscafe.com/text/heisman62.pdf
When you played 6. Bg2 you hung the c4 pawn. However, it looks like 6... dxc4 7. Qa4 wins it back. Plus, taking the pawn would have made your center stronger and given you mobile center pawns. I don't play this variation so does anyone else have thoughts?
You missed a tactic when he played 11... Be6. You could have removed the defender (the bishop) of the knight on g4 by playing 12. Bxe6. He would have to play 12... fxe6 when you could take on g4 with the Queen.
You gave up your bishop for a pawn when you played 17. Rd1. You could have played 17. Bxe6 and been fine.
Yes, 27. Rxg5+ or Bxg5 would have been better. It's a free pawn! I probably would have played Bxg5 because it attacks his queen and the queening square for your pawn.
31. Nf4+ allows him to win a free knight. (31... gxf4)
Nice job with spotting the Qg3#.
Hope this helps.

It's hard to argue with success, but you need not have sacked your bishop,
17 Bxc6 Nxc6
18 Qxc6 and unless I am mistaken, he cannot trap your queen or anything dire.
He did not have to give the piece back as 19....Nxe5 white Q moves 20...Bc8
Granted, black does not like 23...f6Nd2 but it's better then losing it.
28...Nd7 looks good and long overdue, although he can almost get away with RxBe5 29 Nxf6+ QxNf6 30 QxQf6 RxRe5, the trouble is, he is already down a piece so is swapping down to a lost position even though he came out a bit ahead in the combination. 31...gxNf4 leaves him still overly exposed but better off than leaving it unless I am missing something.
Your 32Bg7+ sac was really clever! Well done there! I would have played
32 NxRe6 Qg8 (only way to defend33 Qf6#) 33 Qh3+ Kg3 34 Qh5# which is not nearly as elegant as your bishop sac.
Chess is like golf (also war and poetry), players evaluate themselves by their brilliancies, yet win or lose according to blunders.