This, exactly. I have one variety, Elba, that gets the hollow cavity issue after a lot of rain. They are huge tubers, so I do get a lot of potato out of them.Yes! Even if they had a blemish or looked like a bug started to nibble, if firm then peel, cut out any spots/eyes, and enjoy! Sometimes there can be a hollow cavity inside a potato-maybe too much rain at one point. But, those are fine to eat. So, black and brown or mush on a potato are the things to remove or to toss the whole thing if too much is impacted.
For longer term storage, this is what I do:
Dig the potatoes. Put any that I nick with the shovel in a separate pile. DO NOT WASH THE DIRT OFF THEM, unless you're going to eat them right away.
I put them on these tables on the porch:
That's my garlic, but it's the same set up. The tops of the tables are wire mesh, so there is good airflow above and below. Cover the potatoes with a sheet or other breathable material to keep them out of sunlight. This lets the skin toughen and cure.
In a few days, the dirt on them will be dry and you can brush it off. I wear exfoliating gloves when I do this, and it works very well. I put any that were damaged in digging in a paper bag (again, breathable material that is opaque) in a cupboard to be used first. The rest go in a cardboard box in the basement.
They will eventually sprout; store potatoes are treated so that they don't. Mine last well into winter this way.