Assuming I'm reading the schematic correctly, here's what I don't understand: If it's accurate on the 200mV scale, it should be accurate on the 20V scale as well. They both use the x10 buffer gain, and on the 20V and 200V scales, the input signal is divided by 100 by U1(1,2), R5, U1(3,4). So on the 200mV and 20V scales, 0-200mV is presented to the buffer and multiplied by 10 to present 0-2V to the integrator. On the 2V and 200V scales, 0-2V is presented to the buffer and multiplied by 1 to again present 0-2V to the integrator.
If the divide by 100 is inaccurate, both the 20V and 200V ranges should be off. If the x10 multiplier is off, both the 200mV and 20V ranges should be off.
Could it be something as simple as oxidation on the switch (S7) contacts in the 20V range?