One of the best ways to keep an eye on what is happening around you is with peripheral vision. A lot can be seen from the corner of the eye, especially movement, and it is great way to watch someone without raising suspicion.
It is often shown in the movies, where the aging spy is divulging trade secrets to an apprentice. In most cases, the skills shown are almost beyond belief, and pretty much only possible on the Silver Screen, but there are many items in the world to help you stay aware.
Mirrors or other reflective objects, even windows from the right angle, can be used to watch behind you in most situations. You can also use reflective finishes on walls in restrooms to ensure no one attacks from behind at a time when you are pretty vulnerable, as well as the glass that covers the sports page in many bathrooms.
In most situations, you can use these reflective objects to notice potential threats (every unknown person is a potential threat), so you can assess the person and either dismiss as no danger or prepare countermeasures. And while this is in no way definite, watch for fast motions that can signify bad intentions. Anything that makes you suspicious should be assessed with your full attention.
It may be nothing more someone in a hurry, but if I hear motion coming up behind me, I turn and give it my full attention until I determine there is not a threat. And that is where reflective devices come in handy; they let you know what needs to be assessed.