First off, don't worry about the display wandering around in the lowest two ranges. The 200mV and 2V ranges have an input impedance over 1Gig, so the input will pick up a random charge when the leads are open. 20V and above ranges are the standard 10Meg input impedance, and should zero out with no input.
It's old, so do the easy stuff first, you might get lucky. Disassemble and clean the circuit boards with IPA and a brush. Re-seat the socketed chips. Pull the daughter boards up and off, clean them too and re-seat.
I have a couple of these units. Fortunately they only needed simple repairs to get going, so I never studied the circuit that closely. But I do know the ranging is done with relays, one big one over to the left side, and some reed relays on the daughter boards. Perhaps one has sticky contacts?