New data - After a discussion with an Apple tech, I was asked to not perform a hard reset when the spinning beachball appeared but to wait it out and see if it recovered on its own. This was the result:
Last night I shut down all applications, plugged in my BlackBerry to charge, used a hot corner to blank the screen and walked away.
This morning I hit the space bar to turn on the display, entered my password, got a normal desktop view, checked the Dock to make sure that nothing was running and launched Console. Console opened, Dock froze, spinning beachball appeared (and continued to spin for 30 min). It was responsive to the mouse and the touchpad but otherwise dead. Hot corners were not being detected. I heard the external hard drive spin down so perhaps that indicated that Time Machine finished.
After 30 min the ball stopped spinning and I had control of Console but the Dock did not pop up. When I tried to minimize the window it would not (though the ➖ icon dimmed; when I clicked on the Maximize button I got the spinning ball briefly. For a time neither one (maximize or minimize) had any effect. Spotlight was available. I could not Hide Console but all of the menus seemed to be available. When I tried to Hide Console the screen did not change but the Finder menu showed up; after 5 min the Console window minimized (so it seemed to just be REALLY REALLY slow) and the Dock was again available. Activity Monitor opened and everything looked normal.
After having occasionally checked to see if the MBA had gone South during the morning (it did not, at least not that I detected)- While it was asleep I hit the space bar to wake it up and ------ nothing. After probably 10 min total time the password box popped up. Console was still running and showed no misbehavior; Activity Monitor was still running and showed nothing strange. The Console log seemed so show that Sophos was updating while Finder was unavailable this morning (about 40 min duration between 0658-0738)).
Later while I was typing an email in Eudora I got the spinning ball. The Dock would open for me but I elected not to launch anything and just monitor system behavior. The Hot Corners all worked for about two minutes and then quit, at which point the Dock stopped responding. The CPU monitor was showing but did not show any changes (which I interpreted as a frozen display). The clock was not incrementing. Time Machine did not seem to be running (I could not hear any head motion on the external drive and there was no Time Machine clock motion).
Sometime while I was away, it fixed itself.
Later, with no applications running I launched Firefox from the Dock and got a bouncing icon but no launch. Eventually (after about a minute) the Dock froze and I tried to open a new Finder window, at which point I got the spinning beachball.
Soon after this I really had to use the machine so I did a hard reset, but this seems to show that the spinning beachball is not necessarily an indication of a terminal condition and perhaps just an indication that the OS is not getting many cycles.