Are those "little white warts" the eyes of the tuber? Are they near the stem? If so, they very well may be the eyes of the tuber which are next year's growth spots.

That being said, the tubers from last year will be old and withered, and beside that old tuber ( if it still exists at all) will be the young tubers which will give next year's plants.

Do your research before you pull off more "little white warts".

If you decide that they are diseased, do not store them with your healthy tubers, but discard them. Don't even compost them if your composter does not get hot.

Well, they're not eyes (that's for sure) The eyes I notice are more up at the top of the tuber. These little things are all over the body of the tuber. They're kind of fleshy feeling.

I wrapped these ones up separately just in case they are infected with something. Never know what I'm going to find in the spring. :)