Don't allow just anyone access to your building after lock-up. Ask people who they are here to see, and make sure that is where they go. Question strangers roaming the halls. Report suspicious activity. Don't prop doors.
Some damage is caused by nonresidents.
However, a great deal of damage occurs after buildings have been locked for the evening. If nonresidents are in the building, someone let them in or left a door propped open. Turn in work order requests for items that look unsteady. Don't remove screens from windows. If you are going to visit a friend, call ahead so they can meet you at the door instead of propping it open.