Ok, I don't publish too many of my telecom ideas here since I am working on revolutionizing the phone call for my next business, but here's a simple one.
If you have a large carrier voice mail, such as the voice mail for a wireless company, you should notice if I call somebody and they are not simply busy, but in the act of leaving a voice mail for me. If so, you should break into their voice mail dialog and connect us.
Right now a common occurance is this. Somebody calls, you can't quite get to your phone, so it stops ringing and goes to your voice mail. But there on the phone is the caller-ID. You call them back, and you get their voice mail right away. Why? Because they are leaving you the voice mail from the failed call.
Similar thing when a call disconnects. Who has the duty of calling back. Often we both call back and we both get voice mails or busy signals. While one could develop an ethos (original caller calls back) we've never managed, so the tech could help us.
Easiest when we are both on the same carrier, but in fact this could be done in any tightly integrated carrier voice mail, though you do have to be careful about PBX lines in this case because you might be calling from or to a shared trunk.