I am sure it has already been addressed somewhere on this board…
1990 manufactured home with Miller furnace… staining around all floor vents… well two that were located on vinyl flooring. 
Are they the low spot in the floor?
nothing noticable… two different spots in the home…
my theory was they covered them with an area rug and it scorched or stained them from the heat?
Were they rusted on the backside?
Condensation or wet feet.
I did not remove them…
I’ve seen staining of vinyl when moisture can get at the cut edge.
The moisture migrates between the color or pattern layer and the top sheet of clear vinyl.
See it near patio doors from leaks and/or poor flashing.
Does the furnace have a humidifier?
no humidifier…
Michael I have see this type of moisture before… in fact this was same home…
david… did you edit your post? i received an email notice that reads different from what it says here…
some of the older style vinyl floors discolored around heat sources…this was really common under refrigerators where the compressor was near the floor, the pictures do look more like water damage though and as David asked I’d be looking for a humidifier that may be set too high…no humidifier…I’d be rolling that fridge out to see if it is discolored under there…just my thoughts…jim
I’ll bet that if you take off one of those louvered registers, you’ll find the linoleum curling at the edges. Some sort of moisture is getting under those yellowing areas.
Maybe from mopping the floors and the water is getting under the edges of the linoleum.
The gray stain next to the shower stall is the backing on the vinyl showing thru. This is very common around toilets that sweat or leak around the bottom and other sources of water that seeps under the vinyl. The backing is literally a form of paper, once it gets wet the color shows through to the surface. I know of no polite way to say this but it is usually found on contractor or lower grade vinyls. The other stain looks like a rusty water stain but I am not as certain about that.
I still have yellow stains on my floor, even after potty training a son. It seems that the backers on some bathroom rugs stain white-ish colored vinyl floors.
tom
that is my theory as well… staining from the area rugs placed over the vents… each vent was in front of a sink…
Maybe a corrosion stain from steel registers with low airflow and moisture buildup around registers in higher humidity areas. Due to dirty or clogged evaporator coil. Find most evaporator coils are plugged in manufactured homes due to very poor filtration and lack of airflow casues increased moisture due to slow air movement andair temeprature below relative humidity temperature.