Not that this move order will actually happen, but 12...Nf5 is also pretty bad. Well, pointless at any rate.
12..Bxf3! 13. gxf3 Nxd4 and Black suddenly has a winning advantage.
(Sorry I couldn't find better points, AnthonyCG covered all the important positional ones).
Also, at your(and mine, for that matter) rating, the modern defense really isn't that good. It's slow, positional and boring. You'll learn a lot more about chess if you just played 1...e5 or the Sicilian.
As a novice chess player, perhaps the most popular 1st move is e4. I've been dabbling with ways to defend it that I feel comfortable with. That was until I saw the modern defense. I was able to come up with my own variation that I really like and was wondering if it had been played before or if there's a big flaw in the plan. The goal of the opening is to get white to initiate the dark squared bishop trade while blockading the light squared diagonals with pawns, meaning the king's safety is not compromised. Play would likely not continue exactly as in the diagram after move four but that is the general concept.