So a correction to start with - I looked closer, and I have a 73 III, not a 77 according to the thread title.
I have also tried different leads, and cleaning the sockets, with no change.
A battery has previously leaked a little inside, but it's been cleaned up and there's only some surface marking on one battery terminal.
Anyway, I found some time to work on this suggestion:
Well, if it is behaving on DCV, try noting resistances on each range for shorted leads then with a value close enough to full scale. (i.e: 270
, 2k7, 27k...) We'll try to make some sense of that.
I found the problem wasn't related to near full-scale values, but low resistance values (in all ranges). For the following results, the resulting value is the value displayed after 10 seconds.
320ohm range - shorted leads - 5ohm
320ohm range - 15ohm resistor - 19ohm
320ohm range - 75ohm resistor - 80ohm
320ohm range - 100ohm resistor - 105ohm
320ohm range - 270ohm resistor - 274ohm
3k2 range - shorted leads - 30ohm
3k2 range - 15ohm resistor - 35ohm
3k2 range - 75ohm resistor - 95ohm
3k2 range - 100ohm resistor - 120ohm
3k2 range - 470ohm resistor - 480ohm
3k2 range - 2k7 resistor - 2k7
320k range - shorted leads - 2k6
320k range - 15ohm resistor - 1k3
320k range - 75ohm resistor - 1k8
320k range - 100ohm resistor - 1k1
320k range - 270ohm resistor - 1k5
320k range - 2k7 resistor - 4k
320k range - 27k resistor - 29k
I did try measuring the voltage across the probes with another multimeter while taking measurements, but couldn't make much sense of the results.