Breht, the handyman, came over and examined things this morning. We eventually figured out (we think) that the toilet tank had two serious cracks in it and had been leaking water into the floor for some time; also, as some friends had suggested, the wax seal connecting the toilet to the pipe below it was in bad shape.
So Breht removed the toilet, and pulled up all the linoleum flooring, and I have a fan blowing across that bathroom subfloor to dry it out. Breht says to expect it to take a week or so to dry; then he'll put in new linoleum and a new toilet.
In the downstairs bathroom right below that, Breht pulled the sagging paint off the ceiling, to reveal that a significant section of the ceiling was also soaked. He cut out a big square of ceiling material; the joists in the space between the ceiling and the floor above are wet, so I've got a fan blowing on those as well. Breht says it may take one to two weeks to dry that out.
While he was here, he climbed out on the roof to retrieve a broken shingle/tile, which he'll cement back into place soon. I'm lucky that the torrential rains the other week didn't get in.
(Have I mentioned lately that Breht is an excellent handyman? If any of y'all who live around here need someone to fix stuff around the house, I'll be happy to put you in touch with him.)
Anyway, all of this could've been lots worse; the whole house could've been flooded. (As a certain Doctor recently put it, "Water always wins.") And I was going to replace that linoleum eventually anyway (but that probably would've been a few years from now).
Still unfortunate timing, because I have a guest arriving in a week; having the upstairs guest bathroom unusable and the downstairs one in disrepair will make the guest experience less enjoyable than it might otherwise be, alas. But then again, the timing could've been a lot worse, too, like if this had happened during a time when I was out of town for a couple weeks.