The quick answer is to not trade unless it gives you an advantage or takes away an opponent advantage. Keep the pieces on the board until you have a pawn up or position or something that makes trading in your favor.
16) Ne5, all it does is clear minors off the board. 23 helps black twice, it give up your bishop pair and allows him to block the pawn.
38) a4 is your last chance to avoid draw I think. Black eventually must respond and your king is more active, you can play to try to trade rooks, your king gets his d pawn and your pawn walks home? Trade pawns and its over.
This is a game I played recently in an OTB team tournament against a lower-rated opponent, and it's the only one I'm not entirely comfortable with (even though I lost more than I won). The problem isn't so much that I think I played particularly poorly, but that after an unexpected opening (4...d5) my opponent always seemed to make exactly the move I was expecting and I was unable to think of any plans other than exactly what happened in the game.
Aside from move 30, which was a simple miscalculation I saw when going over the game with another member of my team, even the computer analysis does not venture beyond a half-point to either side. I don't expect every game to be a tactical extravaganza, but surely there are some ideas that I missed in the game that could have at least steered it into more complicated waters?