It could also be cold solder joints.
I just tonight found one on the power switch of a HP DMM. The DMM was working (I opened it to proactively replace capacitors, though all of 1990-era capacitors seem perfectly fine and even had epoxy end-seals....). Note that you don't want to automatically reflow all the resistors since that'd heat them up and likely disturb the calibration of the instrument. I've also found bad joints in 33120A signal generators (output power transistors, failure causing the output to be clipped). I mostly find bad solder joints on large-gauge leads (switches, transformers, power transistors, etc).
Dirty relays does sound likely. In addition to cycling ranges/modes, you may also want to cycle it from front to rear terminals a few times.