What’s wrong with my sweet potatoes?
Using a Google image search for 'sweet potato disease', it looks like Streptomyces ipomoea:




  Host range and distribution:
  Sweet potatoes; Ipomoea batatas; found in all major sweet potato production regions in the U.S. and Japan.
  Streptomyces soil rot or pox is a widespread disease of sweet potato in North Carolina that results in a reduction in plant growth and severe yield losses.  It is caused by the soilborne filamentous bacterium, Steptomyces ipomoea, and is able to persist in soil for many years in the absence of sweet potatoes.   Fibrous roots and storage roots are infected in the field and symptom development varies based on the timing of root infection [...].  Disease is favored by dry soils with pH above 5.2.  


If you are cultivating your own, this is what that article recommends under 'Management':


  Disease development is favored at high pH.  Have field soil tested regularly and select fields with pH 5.2 or lower.  Develop long-range crop rotation (3-4 years) in infested fields.  Treat soil with a broad spectrum soil fumigant containing chloropicrin 2-4 weeks prior to planting.