The Bad News...
This is a common problem with old wood.
While the common culprits (wax/finish/solvents) can be addressed by stripping, mineral spirits, sanding, ect, it is impossible to know what organic compound came into contact with the wood throughout its' lifetime when the original protective finish had lost its' protective properties.
I once spent hours sanding a 100+ year old hope-chest I planned on refinishing. The first coat of sealer revealed a number of dark "spots" that were not on the wood prior to sealing...bummer.
You have several options. You can use any number of "strippers" to remove the finish you have already applied. Then sand, then reapply. THERE IS NO GUARANTEE YOU WILL NOT HAVE THE SAME PROBLEM as some other chemical(s) can have seeped into the pores of the wood that are simply resistant to removal.
My first choice is a "cover-up." I simply covered the dark "spots" on the hope-chest with a cushion that I (earlier) did not want to use. On a door, you can consider hooks, a mirror, a taseful decal, hanging light, ect.
When I had a similar poblems with one of my doors I simply mounted a number of hat hooks to a scrap peice of teak and attached the teak board/hooks to the door effectively covering the spots.