So we took him to the vets last night. Long story short: he has fleas, explaining the bare spots. Vet gave him flea topical cream, which we need to give him monthly (rub the contents of the little tube onto the back of his neck, where he hopefully can't lick it off--but if he does, it's not harmful to him). I bought flea spray and sprayed around the litter area, where, now that I think about it, I have noticed some small-insect activity. If anyone notices anything that might be fleas, the spray is on the floor in front of the television.
They ran a blood test. Not surprisingly, he has high blood sugar, probably indicating diabetes. So we're switching him to canned cat food that is high-protein, low-carb (fortunately, found a website that summarizes this info for commercial cat foods). Tess will get this, too, it being almost impossible without a lot of effort or creativity to control who eats what (suggestions are welcomed, though). They'll get 3 cans per day. Another blood test result was a possible kidney infection, which we're not dealing with for now. The final result, which worries me the most, is elevated calcium levels, which the vet said could indicate lymphoma. I'm afraid to google on this, from his demeanor when he brought this up. But he said it could just be a random fluctuation. We'll take Otto back in a couple weeks for another blood test, where his blood sugar will be lower and everything else will be OK.