lots of great answers here, there's something else that people haven't considered though:
We perceive depth using a concept called Binocular Disparity. What this means is that we get two different images through our eyes, and our brain merges the two into one image, perceiving the difference as "Depth". The greater the shift in location horizontally between the two images (in the human case where our eyes are horizontally separated), the further away the object is.
Now, we learn just how far away an object is through trial and error. This is difficult enough, but it's made easier by the fact that the relative position of our eyes to each other is constant... oh. Woops. This guy now has a serious problem. If he wants to figure out how far away something is, he:
- Has to have both eyes "looking" at it.
- Has to know what that specific disparity amounts to in terms of distance depending on how he is holding his hands.
Say what? Well, if he holds his hands out wide, the disparity between the images from the two eyes will have a greater shift than if he holds his hands close together. And that's assuming he's good at holding his hands on a single plane. I have no idea what effect it would have if one of the eyes was at an angle. Let's not even start thinking about how you'd keep track of the mechanics if their hands were moving!
That's hard enough to write, let alone to do. That's an immensely difficult calculation, and while he'd probably learn to do it instinctively to a certain extent (brains are amazing), the chances are that they'd have to develop a coping mechanism whereby if they want to judge depth they move their hands into a "known configuration", like, hey, holding their hands in front of their face. Funny how it comes back to that.
There's something else related though that would be even more weird:
I hold one hand with the eye facing in front of me. I hold the other hand with the eye facing backwards. Result: AAARRGGGGHHRHGGFGGHR * brain melt *.
There's something else weird you can do to screw with eyes, that's called Binocular Rivalry. It's where you feed two different images into the eyes and watch your brain struggle to figure out wtf it is looking at. Generally, people either have a "dominant eye" which comes out on top, rendering you blind to the other image, or they find their vision switching between the two as they fight for dominance, or in really weird situations, the brain tries to merge the two images together into one seriously screwed up combination, depending on how similar the images are.
Now, this happens because our brains expect very similar images. It's likely that a species that didn't evolve with such a convenience would likely develop a VERY different brain. Maybe they'd even split the images coming from the two hands into different processing nodes in the brain, and maybe they could even see in two directions simultaneously. That's going to result in a being that on a psychological level differs massively from humans. It's also likely that they would treat the input from the two eyes independently, and on the whole they'd probably be epic ad multi-tasking. On the other hand, they would have hardly any depth perception at all, having to rely on visual cues like shadows and partial obscurity behind other objects to judge distance.
I'll tell you something, camouflage clothing becomes amazing under those circumstances. The chameleon would be their worst nightmare. All you'd have to do to sneak up on them would be to have a bunch of tall people far away and a small person walking up a lot closer, they wouldn't know till the last minute that one of them was a lot closer than they thought.
Death by Parallax. Awkward.*
*Yeah, alright, they'd probably develop other coping mechanisms for judging immediate proximity. But that isn't as funny.