In this game, I faced an opponent that was not up to the task of defeating me, although I think I should have lost. This has happened a few times in a row now, so I need a little down-to-earth criticism to keep me from getting too cocky.

Pound away!

Criticism: Your choice of opponent's is horrible. Presumably you are posting your game looking for criticism so that you can improve. If your goal is to improve you must play higher rated opponents.

 

"I think I should have lost"

What in this game makes you say that? Your opponent neglected developing his bishops and started giving away material on move 9.

 

"Another idea I had was Nxb4 Ra3 Nc2+ winning the rook!?"

Criticism: Failure to play your good ideas. Also, failure to calculate the line accurately. Since you have a loose bishop on e7 in that line, you have to calculate what happens to it. For example 13. ... Nxb4 14. Qxe7 Nxa2 you are up the exchange. 13. ... Nxb4 14. Ra3 Nc2+ 15. Kd1 Bxa3 you are up a whole rook.

At the start of the game, he had a rating of 1300 and I was 1312. Figured it to be an equal game with the black handicap for me. But point taken, thank you.

 Perhaps "should have lost" is a bad choice of words. "Lacking game" would be more accurate.

I wasn't sure if Rfe8 was a better move then Nxb4, but I am now. It puts a second question to white, and on move 14. he can't save both his queen and rook. If white did try for the exchange variation you gave (granted, I did not see it!), I'm winning more then just an exchange with Rfe8!