Thanks for your replies! Actually, I had already selected one of the objects (the Double Bed 13.gsm) and then gone into File->Libraries and Objects->Open Object...
Then in the main object window (which was the [Read Only], as the library was the .lcf) I clicked on Details... at the top, and in the next window I checked the box 'Hotspots on bounding box'.
Then I went to save the object, but with it being a [Read-only] file I couldn't, so I discarded the changes. BUT...
Now, in my plan window, the same Bed Double 13.gsm was showing with all hotspots on all corners. Even more strange than this, other objects in the plan also showed all corner hotspots when selected, even though I hadn't even touched them. As if some sort of trigger had been activated when I went into that one object (the Double Bed 13) and switched the behavior for all objects.
Then after some time working with the project I closed it. I worked on something else, with different libraries.
When I went back to the same project and loaded it and its libraries, object behavior had reverted to only showing 2 hotspots. I had to once again select an object on my plan, then File->Libraries and Objects->Open Object..., go into the Details... dialog, check the box 'Hotspots on bounding box', close the object without saving and once again all objects in my plan display all hotspots.
Rather flakey behavior for ArchiCAD, I would say.
MacBook Pro 17" 2.4GHz, MacOS X 10.5.6, ArchiCAD 11 & 12, WinXP, Vista (well, not really Vista...)