Should I worry about old carbon-comp resistors?

I never heard of leaky film capacitors, but leaky antique paper capacitors are quite common.

You don't need a lot of leakage in a coupling capacitor: when there is 200 V on one side and a 1 Mohm grid leak resistor on the other side, a 99 Mohm leakage resistance will already disturb the bias point by 2 V.
 
ESR is not indicative of leakage, but is generally more suited to testing electrolytics used in power supplies.

For leakage testing, you need to apply close to the capacitor's rated voltage and measure how much current passes through it.
Not convenient to do as a bench setup, but many testers have been sold for this purpose, ie Heathkit, Sencore, Sprague etc.
I use either a Heathkit IT-11 or a Sencore LC53.
 
Back to original topic. The US military caused an upgrade to RCR07g carbon comp resistors about 1961, to prevent moisture incursion and value drift. This was a secret, not documented anywhere. Allen Bradley and Sprague produced carbon comp resistor sold to businesses on the same lines as the military resistors. I, and an organ/guitar amp tech in NC, have noticed that CC resistors post 1961 in dynaco, US made (only) Hammond organs, and HH Scott equipment have CC resistors that don't drift. Unless tha paint is damaged by overheat or phyical damage. You can't tell the good ones from the garbage by looking at them. Sounds as if Heathkit was buying garbage grade CC resistors. Considering their market position and reputation of their sound equipment, I'm not surprised.
Paper caps were the standard pre-1960. They had no adjective, just no plus on the lead that electrolytics have. Changeover to mylar was gradual from then, ending about 1970. Polypro and polystyrene came later. Mostly mylar caps were forever, but some vendors had trouble spraying the metal or locating the metal foil correctly that caused their capacitors to leak. French SCR was one brand condemned on this website for garbage film caps.
Some paper caps were wax dipped, which stopped moisture incursion within temperature limits. I replaced some GI paper caps in a dynaco PAS2 for bad sound, finding when I replaced the last one that the kit builder had burned the wax coating on one cap. He hid the damage by putting the burned spot on the bottom. @#$)(*& There was nothing wrong with the other 11 GI caps. The mylar caps I replaced the paper ones with, sound funny.
 
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I routinely go with metal film resistors and no matter if I’m replacing 1/4 or 1/2 watt I go with 1 watt resistors. They have higher voltage ratings and for a little more money it cheap insurance. Lots of people like CC for grid stoppers but I’ve never had a problem with MF there as well. if you have your heart set on CC make sure you heat them to about 150F for 30 minutes then let them cool on a ventilated surface. Remeasure them for value as they are notoriously off value if they are vintage. Large CC are usually noisy and when replaced with MF people are amazed at how quiet tubes can be. Back in the hayday of tubes hiss was just part of the deal. Turns out most of that noise was the CC resistors! Some claim MF are bright or hard sounding but that is usually because they are used to the duller sound of CC. Ymmv
 
My standard of accuracy, is that piano LP's & CD's (usually containing Steinway grand pianos) sound like my Steinway piano in the next room. The repaired PAS2 failed this test. After the failed dynaco PAS2 repair, I installed an op amp disco mixer (Herald RA-88a) for $15, which was undistorted but had too much hiss & hum as bought. After a 18 months of experiments, I expunged the hiss & hum due to power supply revisions, op amp replacement, and oscillation extermination.
I bought polyprophylene .018 uf caps, plus .0018 caps to parallel, to replace the .20 uf paper caps. The bad sounding mylar caps were .022 uf. Unfortunately due to the high resale value of dynaco equipment, my local unemployed house painter carried the dynaco equipment off to his fence (who obviously instructed the thief what to steal and what to leave in place) in 2020. No more dynaco experiments; hulks on ebay are too expensive. I really miss the FM3 tuner, which fuzzed out in the 80's and lay ignored for 20 years until the service manual became available for download on diyaudio about 2019. The burglar left the no-name mixer which was garbage until I modified it. He took all the Peavey sound equipment, which was upgraded with new electrolytic capacitors and some detail repairs.
About 1961 dynaco equipment. I found the replacing CC resistors above 100 kohm with metal film was useful for reducing hiss. The ST70- had the plate 220 kohm resistors replaced to metal film with blatantly obvious hiss improvement. The PAS2 didn't have a hiss problem.
 
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There's no doubt that carbon composition is a horrible resistor type but I still wouldn't replace the resistors unless the equipment has failed or drifted out of spec. Unless you're looking for a project. Then replace away. Go with metal film types with a high enough voltage rating to survive in the circuit.

Tom