Thanks as always, Eric. I went to the first of the links you provided and tried each of the three possible solutions given there. Neither the Disk Utility one nor changing the Refresh Calendar setting from Push to anything else worked for me (NB: Mountain Lion). But the third suggestion, 'I just found a work around.If you create the event and keep the default calendar (i.e. "Work", or whatever it selects by default), it works, then double click it and change the calendar to whatever you want (i.e. "Family"). Kind of a pain, but easier then entering everything a second time' did work.
On a whim, I then tried changing my default calendar from 'Personal and Home' (which is independent of email accounts) to one of my email accounts — and lo and behold, that worked, too, or has done so far! It is still a bit of a nuisance, because it means changing the calendar every time I enter an event. But at least I can make that change (a change which I quite frequently had to make anyway when an event did not fall into the 'Personal and Home' category) at the time of entering the event, instead of having to enter the event, close the dialog and reopen the event by double-clicking on it to then change the calendar.
I hope this will work for others, too.