The Cooking forum might have some ideas for you.

A photo might help too...

Here ya go with the photo. The spots only come off with a mix of baking soda/water. Maybe the dishes have just given up. We've been using them every day for several decades. I just don't throw things out until they die. :) You can see the tiny cracks in the in the bowls too. Maybe those have something to do with the stains? These close-up pics make the entire bowls look worse everything than they do in person.

Thanks for those possibilities, floraluk2! I read up on "crazing" and it sounds like the only health problem might be bacteria that gets into the cracks. We don't seem to have issues from that though. I know lots of people would have thrown these out a long time ago, but like I said, I choose to use things until they are totally dead. haha I try to think of how the earth feels about things that get thrown "out"......and thrown out too soon. Thanks again for your input!

Ceramics are one of the least environmentally damaging things you can throw out. If they are crazed there's a possibility that one of these days they'll just break in use anyway. I'd repurpose them under plant pots or something rather than eating off them. They'll only get gradually worse and less hygienic.

Thanks floraluk! I have appreciated your input. :)