Monitoring local chat is a very simple, effective means of determining the presence of war targets, criminals, bad-standing capsuleers, and potential spies (ie. the unknowns, NPC corped members, etc).
The presence or arrival of a (potential) hostile player should put you on the defensive. Depending on the nature of your fleet, you may want to align to warp or even dock or leave the system entirely. In particular, if you are operating solo or are otherwise poorly defended, you might want to dock or leave the system lest you get ambushed and have no means of escaping alive.
You should be monitoring Local at all times. Under no circumstances should it ever be closed, even to temporarily switch to a different channel. The most effective way to monitor local while taking up the least amount of space on your screen and always having it on is to have the local window placed on the right side of the screen at maximum height, minimum width. That way, you can see as many names as possible in the local channel. The actual local chat is not important; you are welcome to cover it with the usual windows (Overview, Station services, etc), but it is easy to look at by simply clicking anywhere in the list of capsulers in channel.
One of the nice things about this set up is that you can hover over the capsuleer list and scroll with your mouse wheel without making that window active first (ie. you don’t have to click it and pop it up in order to scroll the list).