Update 5/4/215: I sent these photos to a local expert who replied “Wow, what a bad eye infection! It is actually referred to has House Finch Eye Disease as this disease is quite common in house finches, it is a form of conjunctivitis.”
I was photographing birds around the feeder and birdbath today when I saw this male finch that has only 1 eye. He was getting around well, drinking and eating.
Dagny's Desk 