I just purchased a 1969 Les Paul Professional (low impedance pickups).
It plays very nicely. However, on the 22nd fret on low and high E strings,
it plays the same note, same pitch, down about 3 or four frets. Then it
sounds the regular notes for those frets. I figured that this was an intonation
problem. I was planning on bringing it in for a setup. No problem, right?
Curious, I took a phillps head screwdriver and opened the truss rod cover.
Upon removing it, I noticed a brass nut that looked like it had been adjusted
at some point. But then I also noticed that there was what looked like a hardened
opaque adhesive under the nut. It looks like its been there for quite some time.
I didn't dare try to adjust it. I've seen a few truss rods in my day, but I've
never seen this before. I spent over $1300 for this guitar. I'm scared.
Any help on your part would greatly appreciated.

It could just be that the 22nd fret is too high, so when you fret the notes lower, they hit that fret. The fret 3 or four down from it could also be a bit low. You can take it to a shop to get the frets sanded or put new frets in.