@Darrin,
@AnyPoneDrawn : I found an appropriate plugin and installed it, though I've not finished configuring it. It's the largest plugin we've installed to date.
Since it can potentially allow members to cause emails to be sent to other members, I've disabled it for "Newbie"s (0-49 posts) for now.
Question: should it be opt-in or opt-out to receive emails when mentioned by someone else?
Also: let me know here if the site blows up or things start breaking, since it might be the plugin ;)