The vapor is liquid, vaporized, droplets. It doesn't turn into smoke, oxidized solids. You have to imagine, most of the droplets get carried away with moving air but some will certainly accumulate on surfaces. Mostly benign since the nicotine breaks down quickly but it's there. Eventually it will dry out or evaporate, becoming microscopic bits that mix with dust. The actual volume of vapor will be minute, unless you vape a 30ml bottle in a very short time in a very well sealed room. I'm no scientist but I am assuming the quantity of vapor most people produce is carried away rather quickly with ventilation.
I remember running a fog machine in a friends apartment until we couldn't see. We never noticed any residue. That was a lot of vapor! Also we had no idea a fog machine might be dangerous, two cats in the apartment never suffered ill effects and we didn't either.