You've probably heard the saying "a poor craftsman blames his tools". Well, soldering is a big exception to that saying. Having a nice high and variable power soldering station (vs a $15 soldering gun from Kmart) will make all the difference in the world especially when soldering to the back of a pot body where there's a significant heat sink. Not a huge deal on the pot lugs, but on the pot body, yep.
I would also echo others comments, the bridge volume pot has some pretty messy solder work on it. Might have been some after market work on that pot. I wonder if that work over heated the pot internals and messed up the resistance values a bit. Just thinking out loud, but I wonder if it would be worth while taking the bass to a Luthier and having them check the values of each component to see if everything is in spec.
Or possibly just dropping a new wiring harness in the bass (might actually be the cheapest route)...
(Gibson) Thunderbird Bass Wiring Harness, Treble Bleed, No Load Tone, 50’s or Modern Wiring | String Switch Noise | Reverb