[1.05] Weird issues: Can't build in city + Unit designer

I've encountered a couple of inexplicable issues in my current save game.

First is that I can't build anything in my second city that I conquered off the Magnar, despite having plenty of gold, materials, and building space. Five turns previously (the last time I tried to build anything there) I was able to build just fine. The only occurrence of note that happened since then is that my influence border in that city has expanded. I can build stuff just fine in my first city. I've not had this problem in any of my other games, nor would I have any idea of how to reproduce it.

Second issue is that I've designed in previous sessions no longer seem to be appearing in the unit designer when I research the appropriate techs. In previous games in this exact same install/version, the units that I've previously designed would show up in the next game. I've encountered this problem before in a previous game, although at the time I just assumed that I'd mis-remembered what items I'd given the unit in question. It wasn't until I checked the unit XML later on that I realised what had happened, by which time I'd deleted that save. (I'm a serial restarter. ) It may be interesting to note that in that previous game, unit designs had been appearing just fine, up until that one particular unit. Now none of my units are appearing.