Despite these apparent vision problems, when seen using binoculars, a telescope, etc. over-top his eye-patch, there's an image of a perfectly functioning eye (with eyebrow) in the lens of the device, which even blinks in unison with his non-covered eye.
Peanut - He was hired by Harvey to be his legal clerk; this character is modeled after Birdboy, who appeared in several episodes of the original Birdman cartoon.