Eventually, this Three's Company-esque situation was cleared up. Logan only had a small cut on his right pinky finger. After I got home, I got to clean up the glass, and then after he was put to bed, I got to pull the rest of the glass out of the frame.
I got angry with Logan, not because he did it, but because he could have seriously hurt himself. Of course he doesn't recognize this fact. Ugh, just another fun experience in the Adventures in Parenting.