Ceiling right above the shower or tub is the most common spot, followed by the exhaust fan cover, window sills and trim, the wall behind the toilet, and the base of the vanity. Grout lines and the caulk where tile meets tub often darken before anything spreads to open wall or ceiling surfaces.
Towels left to dry on a hook instead of a bar, a bath mat that never fully dries between uses, or a hamper kept in the room all add a little more moisture to the air on top of what the shower or bath already puts out. None of these cause a problem on their own, but they add up in a room that's already working hard to dry out.
A closed door keeps steam trapped after every shower, and along the coast the air coming in isn't dry enough to help much even with the door open. A fan that runs for a minute after you shut the water off, rather than the whole time you're getting ready, usually isn't doing its job.
A guest bathroom that only gets used occasionally can be just as prone to trouble as one used daily, since it dries out even more slowly between showers. A quick check every so often, even if nobody's living out of it, catches a problem before it spreads across the ceiling.