Most of the time it's the way the nut is cut IMO.
The les Paul's I have, in my case a Gibson flying V being the worse offender.
any guitar were the strings flair out after leaving the nut and going to the head stock, tuning issues especially the G-string.
Needless to say most nuts are cut straight, so in essence when the string flairs out its going around a corner the G string being the thickest unwound does not react well, kind of like a bend.
My tech has a different approach he rounds everything out a bit were the strings flair out from the nut, notice no hard bends.
Notice the way the nut is cut in my shit photo's of my Flying V, no hard corners.
It does not make everything 100% but cuts down on tuning problems dramatically.
I have had the V since 1986 and have had a shit load of people go over the guitar to help with it's tuning issues, never really helped.
Never played live with this guitar because of the tuning.
I know, why didn't I sell it?? Well plays great, sounds freaking amazing, and its a beautiful piece. So used it at home and in the studio.
Four years ago I find a new guitar tech and while picking up a guitar I was telling him about the V which sounds amazing and if your lucky might stay in tune for 3-4 songs and that fine tuning the thing was a bitch and a half.
A few months later got him to do work on another guitar and took the V with me for fun long story short i left it with him and he put on a new nut.
It only took 20 + years but problem solved! I'll play a set with the V now stays in tune way better and if I do need to make adjustments, it's not fighting me anymore.
It's such a minor thing but works!
This is a graphite nut on the V and also have a graphite on one of my Les Pauls and a Takamine acoustic I have. My other Les paul has a bone nut however it is cut like the others.
John