I would start with the calibrated eyeball. The AC line cord connects to a small circuit board with two choke coils and four disc capacitors on it. Any sign of stress or damage, cracks or scorch marks are what you're looking for. These parts can become accidental surge arrestors if lightning strikes a nearby utility pole. But if they get scorched and create leakage current to the radio's metal chassis, this is a hazard. The radio does not have a third prong on the power plug.
If you can plug it into a GFCI-protected outlet, make sure the antenna coax is grounded, and see if connecting the antenna trips off the GFCI. If it does, the radio has a leakage-current problem.
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