The big question is not if you pay attention but at what point you label someone a potential risk and how that impacts your actions.
Some good stuff above (mixed in with some nonsense too, of course - the nature of online life!) about assessing the situation on entering a store or new environment.
A few people have responded as if this sizing-up has to take a bunch of time, or as if it necessarily involves ... suspicious ... body language on the part of the person looking around. It does not need to do either of those things.
I'm a big fan of paying attention to the people around me in a normal, everyday sort of way. When entering a store, for example, look around as if looking for the clerk, then make eye contact and nod. Nothing out of the ordinary there. You can look around much more slowly and more completely before asking where the bathroom is (and if the sign is large and right there and bloody obvious, so what? They get that question a dozen times a day anyway, and nobody thinks it suspicious that a person might look but not see even the most obvious sign.) These are normal interactions, not outside any norm that I ever heard of.
If someone else in the store catches me looking at them, a brief nod & smile in their direction (perhaps even a voice greeting, depending on the part of the country I'm in) easily takes care of it.
As for
whether it's good to look around in the first place, I'd say it's downright foolish not to. It's weird that people are pinging on this as if it were a bad thing.
***
Signs of things maybe going south:
People out of place, doing things that are out of place for the location.
Nervous twitches, bouncing on the balls of the feet while looking around with quick darting glances.
Hands that clench and unclench at a person's side or in a hoodie pocket.
(Both of those are symptoms of adrenaline dump, plus the darting glance thing is often a check for witnesses. People looking to assess tend to have a more calm, smooth eye and face movement.)
Two people entering the store together while a third one stays outside (esp if outside person has the nervous twitchy looking around thing going on).
Car backed into a spot near the front/side of the store with the engine running.
A person leaning against the outside of the building doing nothing in particular with one knee up (foot flat against the wall) and looking around -- especially if two or three other people are talking to each other nearby. That guy may be a lookout for the drug deal, with a quick access weapon held in the crook of his knee. This isn't necessarily a sign of impending violence inside the store, but definitely a sign you want to shop elsewhere.
***
As for actions taken in response to most of this stuff, I'm a big fan of being elsewhere when it's reasonably possible, and in a probably-okay situation I'm a big fan of getting to a place where I can
quickly and easily leave while I look for more information about what's going on. I'm also okay with never knowing the end of the story. Drive away...
The world is not going to come to a screeching halt if I decide to pay at the pump and not enter the store at all. Or if I decide to sit in my car for a few minutes before I go into the store. Or if I decide to leave the store abruptly and come back after the question mark has resolved itself.
pax
"Many victims of violent crimes have stated that they knew there was a developing problem, stating that they could ‘feel’ it coming, yet they ignored their ‘emotional instincts’ and subsequently became victims. Other victims never saw anything coming even though afterwards an in-depth debriefing showed that danger signs were evident and should have been recognized well ahead of time. I’ve personally interviewed such victims many times over the years. Other victims have clearly observed evidence of a potential problem yet chose to ignore it altogether. A classic example of the latter occurred in Southern California in the early 1980’s. Customers inside a McDonald’s restaurant observed a man in the parking lot standing beside a pickup truck loading ammunition into weapons and placing them in his waistband and then obtaining more firearms from the pickup truck and walking toward them. Yet the customers continued to sit and simply stare at him, as if they were watching a bad movie but couldn’t walk out of the theater. The gunman entered the restaurant, where he killed and wounded many patrons. Simply walking out the opposite door would have saved them, yet they chose to ignore clear evidence of a developing dangerous situation." – Scott Reitz 
