I cast my vote for tossing the old panel and installing a new SQD one.
Sometime in the future, you are going to have trouble with those breakers and if Murphy has any say in it, (and when doesn't he?
) it will be at the
most inopportune time!
I can't say for sure from the pics, but do the wires going to the 50 Amp and 30 Amp breakers look undersized? You can run a little bigger beaker (than you would normally use on any other circuit) on a dedicated welder service because of the duty cycle but that looks just a shade small to my old eyes even at that.
It would be interesting to see how the wires to the receptacles are connected in the outlet boxes. You might want to consider changing them all out too if they are "old as the hills" and they really aren't expensive at all...depends how well they grip the male plug-in or if you see any sign of a hot-spot on them.
The main problem certainly sounds like a bad neutral somewhere. A good electrician should be able to track that down right fast!