I made a lot of mistakes, but so did he. I missed a good move on 22 due to Ne2+. I was too in love the idea of forking two rooks and the king all at once.

[Event "ICC 45 20 u"]
[Site "Internet Chess Club"]
[Date "2009.02.04"]
[Round "1"]
[White "clalauquen"]
[Black "Moe"]
[Result "1/2-1/2"]
[ICCResult "Game drawn by mutual agreement"]
[WhiteElo "2398"]
[BlackElo "1322"]
[Opening "Petrov: classical attack"]
[ECO "C42"]
[NIC "RG.04"]
[Time "18:00:41"]
[TimeControl "2700+20"]

1. e4 e5 2. Nf3 Nf6 3. Nxe5 d6 4. Nf3 Nxe4 5. d4 d5 6. Bd3 Bf5 7. O-O Bd6 8. c4 c6 9. cxd5 cxd5 10. Nc3 Nxc3 11. bxc3 Bxd3 12. Qxd3 O-O 13. Rb1 b6 14. Rb5 Bc7 15. Qf5 Qd7 16. Rxd5 Qxf5 17. Rxf5 h6 18. Bf4 Bxf4 19. Rxf4 Nd7 20. Re1 Rac8 21. h4 Rxc3 22. Re7 Nb8 23. Ne5 Nc6 24. Rc7 Nxd4 25. Rxc3 Ne2+ 26. Kh2 Nxc3 27. Rc4 Nxa2 28. Ra4 Re8 29. Rxa2 Rxe5 30. Rxa7 Ra5 31. Rb7 b5 32. g4 Kf8 33. Kg3 Kg8 34. h5 f6 35. f4 Ra3+ 36. Kh4 Rb3 37. Rb6 Rb1 38. Kg3 b4 39. g5 hxg5 40. fxg5 fxg5 41. Kg2 b3 42. Rb5 Kh7 43. Rxg5 b2 44. Rb5 Kh6 45. Kh2 g5 46. hxg6 Kxg6 47. Kg2 Kf6 48. Rb3 Ke5 49. Rb8 Kd4 50. Rd8+ Kc3 51. Rc8+ Kd3 {Game drawn by mutual agreement} 1/2-1/2

Instead of 23. Ne5, Rxa7 keeps you a pawn up. Also, after Nxc3, did you now see nxa2?
33. ...f6 instead of Kg8
48. I would suggest trying to get your king to c2 and keep your opponent's king as far away as possible. Possible continuation:
47. Kf2 Kf6 48. Ke2 Ke6 49. Kd2 Kd6 50. Kc2 Kc6 Now you play 51. Rb3, and Black has to surrender the pawn.
a) 51. ...Rh8 52. Rxb2! Make sure you take with the rook, as it will provide cover for your king. 52. ...Rh2+ 53. Kb1 Rh1+ 54. Ka2 ends the perpetual checks.
b) 51. Ra8 52. Kxb2 Ra5 53. Rc2+ Rc5 1/2-1/2