OK, I had F-Droid 0.97 installed. I asked it to update itself. Now it says I have version 0.102.3 installed. Do you have to advance one version at a time, or what?
I did that, using F-Droid to install/update F-Droid, and it installed, but F-Droid "About" still says 0.103.2. Something in the build or repository is inconsistent.
(Android 4.1.2, kernel 3.4.0).