Some of my Shinseiki Asian pears have brown spots inside when cut open. I don't think they are over-ripe. What else can it be?
It can be brown rot. I would not call that "spots", its more like one big spot. This has been a very bad year for brown rot here and I got some of it on everything including my asian pears (the Europeans got it even worse).
No, it's not one big spot, its a series of small patches of brown in the flesh of the pear. I had it last year, too and thought it was due to leaving them on the tree too long. But these pears were deliberately picked early.
Very frustrating. . .
I am only going to guess that it is bitter pit, a calcium deficiency.
What does 'bitter pit' look like? And how does one correct for it?
It looks sort of like cork and it is by the surface of the pear. Each spot is something like 1/8" or so (bigger or smaller as well). I think Geraldo may have it there; bitter pit is primarily a problem on apples but I have also seen it on my asian pears. One last long shot is stink bugs, but these mainly deform the fruit and you did not mention deformed fruit. See good link below for more information on bitter pit including treatment.
Here is a link that might be useful: bitter pit