fading colours / lightfastness. You need to worry about the lightfastness of organic materials.
problems with varnishing, results in patches/stains of semi-gloss
The Yellowing Of Oil Paints
In my experience, most of the yellowing we see in old oil paintings is in the old varnish, and once that is removed, the yellowing of the paint itself is usually negligible, unless the painting has been recently stored in a dark place.
Linseed oil paints do yellow somewhat, but the yellowing is a temporary phase they go through that eventually reverses if the painting is exposed to light. That being said, the Old Holland Cremnitz White samples on my test panels yellow more than the others on the same panels, and remain yellower for a longer period of time. My guess is that this is due to their stabilizer, hydrogenated castor oil, which the manufacturer doesn’t want us to know is in there.
My personal feeling is that concerns for yellowing of oil paints are overblown, because the initial yellowing of linseed oil paints reverses with exposure to light, as I mentioned in my book. If the painting is kept in darkness, the yellowing will return, but will bleach out again if the painting is returned to the light. How fast these changes occur depends on the strength of the light the painting is exposed to.