One of the first things I learned when I went on ops was about 'retina burn'. Meaning, if you look at something straight on and keep looking at it eventually you'll get retina burn and you won't be able to see clearly. It's basically eye fatigue from staring at one spot for too long.
I was taught to always keep looking around, even if you've got to look at one specific thing intently. It seems weird that if you're not looking directly at it you might miss something but in fact if there's retina burn you can be looking RIGHT AT whatever it is and still miss it. The trick is to 'see' it out of the corner of your eye.
Anyone ever notice how when you see something out of the corner of your eye almost always when you turn you're head there's nothing there? Some say this is a glimpse of entities that we can normally not sense. Could be. Is it also a physiological/psychological effect? Definitely.
It's a natural reaction to turn your head to look at whatever you saw from the corner of your eye, its a survival mechanism. But what if you DIDN'T turn your head? Would this thing stay there? Or would it go away just like if you turned your head? There is such a thing as jumping at shadows, meaning if you're expecting to see something (anticipating or fearful of it) you're more likely to think you've seen if, if only for a moment.
Also notice how people just seem to 'know' when someone is looking at them often times. Like when you're sitting in your car at a light, and you KNOW the person in the car next to you is staring at you. Basically this is (and 'retina burn') were the reasons I was strongly encouraged to develop better use of my peripheral vision. If people think you're oblivious and don't realize they're there you have the advantage. Also, if you're watching someone who's paranoid, one straight look in their direction and it's blown.
I encourage everyone to try to improve their peripheral vision. You'd be surprised how good you can get with it. There IS a limit to how much you can see but it's all about being aware, and seeing something different than what your eye is looking at. And remember, if you stare at ANYTHING long enough it will begin to look like something else- beware of illusions. But that's another topic.
Here's a fun illusion