I have to agree with the other posters, awareness is not paranoia. After a while it does become second nature.
A couple of months ago I was at one of our local guns shops with a friend. I've come to know the owner of the place pretty well over the last several months. He is a former full time LEO prior to opening the store and still serves as a reserve officer and firearms instructor for his department.
While we were in the store a seedy looking fella came in, immediately my attention turns to his as does the owner and his helper. The guy comes up to the counter and starts asking about a magazine for his pistol, and produces a junk pistol, it looked something like a Jennings, from his waistband. No holster, it was just stuck down the front of his pants with his shirt pulled over. The pistol was unloaded so there was no real threat. However it was interesting how the awareness kicked in.
I didn't think anything about it until we were on the way back to the house. My friend commented on when the guy came in. My friend was in tune with watching me, the owner and helper and made comment that all of our attention quickly turned to the customer. He knew I was armed as were the two behind the counter.
As people that choose to be armed I think the awareness is something that is learned in our training. We also try not to put ourselves into situations that aren't to our advantage, however as we all know there is always that one time where the situation will come to you.
Cheers,
Sam