... Figures that almost immediately after posting here, I'd stumble upon a working solution. Per this random forum's thread I tried uninstalling KB2670838 and rebooting, and I got Aero back. Amazingly enough the other two problems were also apparently related, as I have a functional Calculator again, and Photo Viewer displays PNGs just fine.
Edit: Should note that I'm not sure if this also fixed the repair install issue, but I'm not going to bother trying.