I got up this morning to find a small puddle of water on the bathroom floor. (Better than a large puddle of water on the bathroom floor.) As far as I can tell, the fault was that I hadn't screwed on the water hose quite tight enough when I reattached it. I gave it a couple more good turns, and mopped the floor. We'll see what I find when I get home.
I used to have this problem when connecting up water hoses on chemistry lab apparatus: there's a fine line between "finger-tight" and "not-quite-tight-enough".
I also realized this morning how I should have drained the toilet tank: shut off the water, then flush. Tank empties and doesn't refill. Duh.