What do the leaves and stems of the plant look like? If that's late blight, you won't just have spots like that on two or three fruits, there will be black blotches on the leaves and stems as well, with probably some dead foliage too.
If the leaves and stems of the plants don't have lots of blackened areas, see if there is anything in these pics that would be helpful in identifying the problem:
http://vegetablemdonline.ppath.corne...y.html#Blossom
BER doesn't only occur on the blossom end of the fruit. It can appear on the side of the fruit instead, and can also appear only in the interior of the fruit, with nothing showing on the outside at all.