You never know the real chances of disease in potatoes at the store, unless they have signs of disease. I wouldn't recommend just buying them as-is and planting them.
Buying seed potatoes gives you some insurance, and they might come with some guarantee (though I wouldn't count on it).
The main reason I personally wouldn't grow grocery store potatoes is that they could be patented, PPAF, PVP, or genetically modified, and that could cause legal and ethical problems (not only, but especially if you're doing it for commercial purposes).
If you buy organic potatoes, the risk of them being genetically engineered should be minimal, but they could still be PVP, PPAF, or such.
Anyway, PVP only applies to true potato seed, anyway, though.
If you're sure there aren't any legal problems with planting the grocery store or farmer's market potatoes, you can always try to disinfect them, somehow. I don't know that it's ever been attempted, but if I were going to plant them, I would zap them in a jar of water with a Z4EX or some such, first. Normally, Hulda Clark zappers are used on humans, in the realm of alternative health care (not by the medical community), but I think it's less arguable that it would have an appreciable ability to disinfect such as seeds and seed potatoes, seeing as zappers have been shown (not with standard studies, though) to kill and/or prevent microbes in vitro. Once again though, this is an experimental idea, and I don't know if it will work, necessarily.
As suggested in another answer, you can grow potatoes from true potato seed instead, too. It takes longer, but there are many advantages (including, supposedly, less problems with seed-born disease). If you don't want new and unpredictable kinds of potatoes, I don't recommend this unless you use Zolushka potato seeds or some such (which should produce the kind of potato advertised). Other advantages may include ease of storage (real seeds take less space), the ability to breed new potatoes (because every seed can produce a new variety, and you can cross them with other fruitful potatoes, too), etc. The tomato-like fruit they produce is supposed to be toxic, though.
I grew true potato seed, this year. I got four plants. One of them contracted a disease, but it didn't spread to the other three, which were in the same container. The disease probably came from the environment and the genetic susceptibility of that particular potato rather than from the seed, however.