"The reason for my question is that whenever my Retina is off, the screen always looks smeared, even though it always sits on my desk at home and I don't believe I ever touch the screen.
So what is the deal?!"
Sounds like "StainGate" to me.
You used Windex on it?
Possibly with ammonia?
Egads !!!!
In that case, no wonder it's smeared!
The retina displays have a very VERY thin anti-glare coating that is sprayed onto them.
This coating is very fragile by nature. It's easily damaged, moreso in the earlier versions of the coating (such as on the 2012).
Hence, the origins of StainGate.
Apple has (had?) a program of free screen replacements for StainGate, but a 2012 may no longer be covered.
The best way to "maintain" one of the retina displays is to "clean it" AS LITTLE AS POSSIBLE.
DON'T "wipe" it with any pressure.
Just "dust across it" with a soft cloth.
If you get something on it that won't "dust off", then use some water and a moist area of cloth, using as little pressure on the surface as you can get away with, then dust it dry.
Try to avoid touching the surface of the display, particularly when opening and closing the lid.
That's worked for me for 3 years with my 2015 MBP. No flaking.
If the anti-glare coating is already damaged or partially flaked off in some locations, there's NO WAY to "restore it" other than replacing the display.
Some folks have actually "rubbed off" ALL of the anti-glare material as a last resort. The end result is a glossy display, but with no "smears". I would try this only if it was really bad.