When doing a proper clean I clean the kitchen surfaces etc. first, then the sinks in the bathroom, then make my way through the levels of 'dirty' in the toilet (cistern, lid, seat, and so on) and finish by throwing the cloth away.
People who keep separate cloths for each - what do you do with them? Do you wash them in detergent and rinse, leave them in a bucket of something, bleach them, put them in the wash, what? And if you're cleaning a cloth well enough to have it hanging around for multiple toilet cleans, presumably you judge it clean enough to wipe the bathroom sink and the bath/shower each time prior to the toilet? If so, why wouldn't you clean your kitchen with it? I don't think I'd like to 'risk it' with sinks/showers any more than I'd like to with kitchen counters.
Incidentally I have not bleached any door frames, but I do get very brown droplet stains on the white doors/frames if anyone flicks water on them and leaves it to dry. I live in a rather hard water area, though how that relates to brown marks in addition to the limescale everywhere, I don't quite know.