Even if I get nothing else out of this experience, I'll have at least learned a lot of vocabulary pertaining to apartment rentals.
I'm happy to say that I've secured an spot in an apartment after only a few days of viewings! The place is in Kreuzberg (on the Oranienstraße for those of you as enthusiastic as I am about Google Maps).

I encountered two unexpected difficulties during my search. First, I had a fairly hard time finding places with roommates who are still undergraduate (or even graduate for that matter) students. Secondly, few of the people who responded to my calls or emails regarding listings were actually German. Once I decided not to care too much about either of those things, the apartment hunt got a lot easier.
The roommates I'll have are young professionals from Italy and Spain (I can't remember whether she actually told me she was from Spain or whether I just assumed. I'm still thinking of a subtle way to figure out which) [update: she is indeed from Spain]. Their German is about the same level as mine, and they speak only German in the apartment, which is what was most important to me. Enough of my friends here from high school are still around, that I'll get plenty of face-time with native speakers even if I don't live with them.
Here are some photos from the listing for your viewing pleasure. I'll take another one of the room (above) once I've moved into it.

