I notice brown spots like the OP describes, but only in the bathroom, and mostly on the inside of the door. They look as though they are residues of water splashes, and I wonder if it’s from wet hands (the towel hangs nearby). They wipe off easily with no discolouration beneath, so I don’t think they are coming out of the door/wall.
We are on UK mains water, and nobody in the house is or has been a smoker (house has been in the family for 40 years). It’s a mystery to me.