There aren't any wrench flats on the post. The post does have a curved receiver to mate to the bike frame. It is this connection that seems to have a little play. I had considered using a toothpick shim to see if I could keep it from moving, but it didn't seem like the right solution.

I wasn't going to change out any nuts on the front part of the break, I was considering putting a locking nut on the back part (behind the frame).