Generally wirewound pots suffer from 1 oxidation 2 general muck and athospheric polution ( cigar smoke , coal fire fumes , hairspray etc ) bear in mind that there is a handy air pump working away when the speaker is playing . and 3 when the contact becomes bad there may be tiny arcing at the the contact point of the pot wiper.

In my experience for the most part these pots stay in the same position for years and years. Hence the other windings will become dirty as described meaning erratic contact.
I have found that by winding the pot over its full range ( in conjunction with contact cleaner ) many times then the wiper and the windings are effectively cleaned for service.

Sometimes its 10 times sometimes 40

This may be sufficient to clear things up but the fact remains that after 50 years the caps will be off. Inductor should be ok and you can test the resistors. No burning is a good sign. Re solder all the joints.