To improve situational awareness, first you have to improve your observation skills.

One idea to practice is to spend an afternoon with a camera. Take a picture of a scene, then turn around and try to recall as much info as possible, and then compare your memory to your picture. Location of objects, people, clothing, height and hair color: as if you're a crime scene witness. (I've heard that most crime scene witnesses aren't observant enough to provide accurate info.)

When you think you've reached a good lvl, the next step is to look at a scene, take a picture, and quickly make at least three risk/threat assessments. When you look at your picture, make as many assessments as possible, and ask yourself if your first three were the most likely or reasonable. For example, is that skater in a good position to try a purse snatch from that women? With a person walking by a tall building, is there an alcove or other location to protect herself from falling bricks/glass? Does that dogwalker have good control of that toothy dog? (In NYC these risks come up often.)

Gaining good situational awareness is a habitual behavior that takes time and practice - it doesn't happen in a day.

Bluecimmers