That discoloration on the 10K may be an indication of overload or a chemical spill, the coating on these resistors are not very resistant, even isopropyl will soften it up and if you get any on it, it will have to dry out thoroughly but has no lasting effects. You'll have to check the resistor with a high accuracy measurement to see if it is out of tolerance. You can use a contact cleaner like deoxit but do not spray it on the resistors, use a lint-less wipe. Yes there is always some rosin residue left on the solder joints, it is of no consequence. Usually these units require very little maintenance.
I have both a RS925D (part of my 242D) and a RS925A (part of a 242B) which I am going through and giving it a once over. The connections on the rheostat are very important and should be snug (do not over tighten), the resistance element/wiper can be gently redressed with crocus cloth and cleaned. I have found some units with some kind of gooey grease on the rheostat, that attracts dirt, I prefer to keep them clean and dry. These units are more or less sealed in their case, there should be little to no contamination getting in there.
These resistors are wound on a mica card and therefor is somewhat easily damaged, not only the fine wire but the mica so be very careful around them.