Well, a few hours on, and things seem to have settled down. Now this is being called simply a "Border Clash", rather than open war, as I had earlier stated. Note that Israel and Lebanon are formally still at war, and have been for decades.
Another point that I neglected to mention previously is the existence of a permanent UN peace-keeping force called UNIFIL, which is supposed to patrol the UN-designated border between Lebanon and Israel, what is called the "Blue Line". Unfortunately, Israel and Lebanon cannot seem to agree just where that border lies. And UNIFIL was conspicuous by its absence when the fighting was taking place.
AJE now has a more detailed report available. It would appear that I was not the only one expecting this to blow up more than it so far has; Al Jazeera brought Zeina Khodr in from her usual area of specialization in Pakistan and Afghanistan.