Q:

Why human eye doesn't exhibit aberrations?

Eye's optical system is composed of single lens and is capable of producing very sharp results, but if I use single lens (monocle) with my camera I'll get soft image.

A:

Two reasons: A camera objective (made up from many lenses) needs to focus on a plane, not an arc. And we dont see the image projected on the back of our eye ball. We build up the image from features extracted by many neurons with each their specialty. That's why we don't have to show reality to the eyes for us to see the same, we just need to construct something that "pings" the same neurons. Need not be the same. Which is kinda scary - can we really trust what we see? Nope, that's part of why accidents happen.

A:

Simply put, it does, our brain corrects for it.  Among other things, you can't actually see where your optic nerve attaches to the retina and your visual acuity is actually much more center focused than even a cheap camera lens, but because your eyes refocus on the fly every time you change where you are focusing, you don't notice the changes or the lack of acuity.
We also have really crazy image stabilization built in to our brains as well because your eye moves around far more than you realize, and it jumps rather than generally moving smoothly.  Try taking a video of your eye sometimes as you read a page or look around the room.  You will probably be very surprised by what your eyes actually do.

