With the late blight the spots on the leaves initially appear as water soaked spots.* Notice any of that?
http://ftsg.ifas.ufl.edu/LBLDBC.htm
I've not heard of more then one spot on the blossom end rot and it only effects the fruit, not the leaves.
http://ftsg.ifas.ufl.edu/BERDBC.htm
Bacterial spot usually has more damaged spots on the fruit.
http://ftsg.ifas.ufl.edu/BSPDBC.htm
Buckeye rot is another to look at.
http://ftsg.ifas.ufl.edu/BUCDBC.htm
Also look at phoma rot.
http://ftsg.ifas.ufl.edu/PHODBC.htm
This Florida site has more ideas.
http://ftsg.ifas.ufl.edu/DBCLIST.HTM
Newt
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.