My guess is that the pot wiper is either dirty or worn so that it "skips" as it is moved across the resistance element. When that happens, the input to the first audio amp goes open, letting it pick up AC from the same or subsequent audio stage and causing feedback- the "screech" that you hear.
I would first check the wire routing around the volume pot and detector/first audio amp tube- it possibly got changed when the set was recapped. If that doesn't solve the problem, a volume pot replacement might be necessary.