Potatoes showing the slightest sign of rot should never be planted. That doesn't just apply to saved potatoes; up to 0.2% of certified seed can have blight.
I am afraid what Robert said is sadly true. I have seen some fine specimen of blighted potato tubers on potato days. You'd think the organisers would have taken them away quickly, but no!
Certified seed potatoes are potatoes which are low virus diseased, because they were grown in areas where greenfly, which transmit viruses, are not common. Potatoes with virus disease have lower yields than those from certified potatoes. Nothing to do with blight. Blight spores are airborne and land on the foliage and get activated under certain conditions (Smith Periods). Blight can potentially survive in tubers in the ground, but it is the wind borne spores that cause the wide spread problem.
All chitted potatoes s h o u l d be green, that's normal.