I recently finished the following game, in which I think neither player made any gross error until the end. Even before black's final move, computer analysis gives white an advantage of over 3 points (with a material advantage of only one point). So where did black go wrong?

As you said, 7...dxc4 was a mistake.  Nbd7 and b6 would both be better.  I don't think 13...cxd5 is as good as Nc5.  18...Ng5 looks inaccurate as well.  Nf6 and even Nd6 look better.  Black takes way too long to mobilize the queenside and pays for it.

Not quite game over: chess.com computer analysis gives the line 20. Nxf7 Kxf7 21. f5 Re8 22. fxe6+ Bxe6 23. Bxe6+ Rxe6 24. Rc7+ Kf6 25. Rxe6+ Kxe6 26. Rxg7 Rd8 27. Rxb7 Rd2 28. Rxh7 Rxb2 29. Rxa7 with a three pawn lead into the endgame. It gives 20. f5? a question mark because it doesn't seem to find 21. Bxf7, which gives a better result than the suggested 21. Bd5. Then again, since I don't have a membership, the analysis depth is lesser compared to Shredder.

As for cxd5, I wouldn't call it game-losing: it's worth only one point according to computer analysis, and I was up by three points by move 32.

And why would I stick to e4 when I'm much more familiar with d4?

Nice game only one mistake in the ned that is 32. Rg6! and mate in 2 after Rh7 and Rh8 mate

Wow that was an amazing game. I am a pure queen's gambit player and I felt like a learnt a lot from this. Keep up the good work :D

13. d5 gets a double exclam? Really?

Yeah, even the computer seems to think that it was an inaccuracy. Let me change it to !?...