No I wouldn't just soot someone for checking a door only if attached or severely threated as in jumped, knife or similar. I'm going to let the police know not that anything would be done unless they are caught in the act. I know what you mean with all this going on it is sad indeed. I'm going to go though around a month of video this weekend and see how often this is happening or if like once month. If I find out this happens often, I'm will just see about breaking my lease and moving as I'm too old for that crap.
Better cameras help but, ultimately, moving is the definitive solution. A neighborhood going downhill like this
never gets any better in any reasonable time frame, only steadily worse. Let the place go to the dogs without you. Do some research, there are ample internet resources available to find a place where law is still enforced. LOTS of people are thinking this way these days and bailing out of hopeless, declining hoods (or entire states, for that matter.) It's unsettling and a pain in the butt to move, but once you take the plunge it feels good to be taking positive steps to improve your life. At any age ....
