In "People and Places", some of my contacts have a red dot next to their name, just above their standing:
The standing is set as I add a contact but I don't remember ever setting this red dot, and have no idea what it signifies. Furthermore, unlike the standing, it doesn't have an 'on hover' tooltip.
What does this red dot signify?
The dot means you put those characters on your watchlist, which means you will be notified every time they log on or off.
The red dot means the character is currently offline, if they would come online the dot would turn green and you would get a notification about the change.
This almost makes sense but it's not true unless the function is broken. I have friends logged in and it is showing a red dot still. I know they are logged in because they are chatting with me in discord and discord recognizes them.