A couple of times today, I had people chat me (yes! it's a verb!), but I didn't notice for some length of time. How long? Who knows. But I fear it appeared rude when instead I was just unobservant.
There should maybe be a popup in the main screen -- something ignorable, like when the rock wants to tell you something -- that would point out that you have people trying to chat with you.
Also, I think we've talked about this before, but I wish I could see both a private chat (or more than one?) at the same time as the global chat.