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That would mean from move 38 onward a different plan.
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Well, the first thing you need to do is the 'if I go here, he goes there...' analysis because if you end up losing material, positional considerations are usually irrelevant. Perfect example: you thought your choice was between winning a knight outright (32.Kxe3 Nxd2+ 33.Kxd2) and winning a knight for a pawn (32.fxe4 Rxe4). If you can't calculate accurately, you don't know what options you're weighing up so you can't hope to make the right decisions.
As it was, I think you did make the right decision. Winning the exchange means that you have a pair of rooks against rook and knight which, on an open board (i.e., one like this that isn't blocked up by pawn chains) is a massive advantage, as long as you can effectively deal with black's biggest threat, that well-advanced pair of queenside pawns. They're easily liquidated and you have a completely won position at move 37. Your rooks can work together better than his rook and knight.
What you need to do at this point is use your rooks together and attack his king and pawns along the seventh rank. Pick off his pawns if you can. Bring your king in and start to advance your own pawns. Something like 38.Rb7 with the threat of 39.Rdd7 makes him have to spend all his energy defending his pawns. (Of course, you can't play Rdd7 immediately because of Nc5 but, if he moves his knight, you're straight in; if he doesn't, move your d2 rook to the seventh rank by a different route.)
A couple of comments on later moves.
41.Kg2 - Why are you moving your king towards the corner? You need to bring him out into the action.
44.Rdxe6 - Big mistake. Endgames where each side has just a rook and some pawns are very often drawn unless one player has at least two more pawns. As whyBish says, this is especially true when all the pawns are on the same side of the board.
48.Re2 - Good. Lets you get your king into the game. Your only hope now is to force the exchange of rooks, though the resulting pawn ending is probably drawn, too (I've not analyzed it).
Lastly, try not to think in terms of 'points'. They're useful as a sanity check when you're considering a complicated exchange but that's about all. Some examples of trades that are 'equal on points' follow.
B+N for R+P. Often seen in the opening, after e.g. black has castled and white has a Bc4 and Ng5. It's usually to the advantage of the player who gives up the rook - they have two more minor pieces than their opponent, in a phase of the game where rooks are usually stuck in the corners, out of play. Those two extra pieces usually secure an advantage before the rooks can get into play.
Q+P for R+R. In the endgame, and if the player who gives up his queen still has both their rooks, this is usually to their advantage. The pair of rooks can attack pawns and win them unless they can be defended with both queen and king.
In your game, you're asking which of the trades N for R and P for N is better. Both of them give you a 'two point advantage'. However, if you trade N for R, you have the pair of rooks, which are very strong when they work together, and your opponent has only one rook. If you trade P for N, you both have a pair of rooks, which is a more balanced position.
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Kingdave, I thought your opponent would take your rook as well. Then I saw that he did not have to. He got your N for free. For me that is the problem with tactics. Way to many variations and so little time. Good for your opponent to see that. I am not sure I would have been able to figure it out. I now have learned another valuable lessen. Of course there is no maxims in chess, but it might be better to see if you can steal a piece instead of trading. duh.
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Richerby,you said, If you can't calculate accurately, you don't know what options you're weighing up so you can't hope to make the right decisions. I do not want to steal this thread, so maybe you could start a thread and tell us some of your tricks on keeping all of the options straight in your mind. If you choose to do this please let us know where the new thread is. Thanks
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No hijack on the cards, I think, as I have no tricks.  The only way I know is to practise.
In my view, the best way to practise is to get yourself a book of tactical problems and work through them without a board. Remember that solving the problem doesn't just mean guessing the first move: it means seeing the combination through to the end and identifying any interesting and relevant side-lines. Reinfeld's books are a good place to start: 1001 Checkmates is easier than 1001 Combinations so it might be best to start with that one.
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