How to practice observing without looking:
First, sunglasses are cheating. Notice how people with dark (anyone wear mirrors anymore?) glasses both conceal their gaze and draw attention to their stares? The slow steady movement of the head doesn't seem to really rest anywhere, does it. The head in one spot seems to send that view boring into you, even if it's off by a few degrees.
Notice how you can be aware of things that aren't in the center of your field of view. Another thing that takes practice, but there are plenty of opportunities to practice. As I type this, there's a flashing Robar ad at the top of the screen. I can see when it changes out of the corner of my eye. I can see more detail while I'm still looking off a bit. I can read it, even when I'm looking a few lines down from the actual text. If you watch TV by looking at the corner of the screen, you can still follow the action and describe the characters, right? Off to the mall, where you scope the babes (or hunks, I'll be an equal opportunity whatever I am) without ever staring. An associated level of discipline here is not having your head snap and lock on when something really interests you--you track the approach and departure of the person without looking at him/her. Describe what he was wearing and carrying in his hands without having stared (look back for confirmation).
A similar drill is to look at the individual for a second, a second and a half (thousand-one-thousand). Now, give a description: sex, race, age, height, weight, hair, eyes, clothing, tatts, jewelry. What hand does he use (where's the watch, where's the cell phone, what hand is the bag in)? Is she married (ring, of course)? What store did the bag come from?
(These are observation exercises, you can work slight variants to make them KIIM games. Keep It In Memory drills are things used by scouts and snipers to improve their ability to report.)
But you're learning to do all this without being seen doing it. As Russ said, slow and smooth head movements. No staring, no jerkiness. After you have the concept based on your observations of the general population, you use those broad scans to find trouble and then these more directed looks to analyze if it's really trouble. Can you spot Loss Prevention at WalMart?
"To spit on your hands and lower the pike; to stand fast over the body of Leonidas the King; to be rear guard at Kunu-Ri; to stand and be still to the Birkenhead Drill; these are not rational acts. They are often merely necessary." Pournelle