A related problem is not fixed.  Perhaps this should be a separate bug report,
but I'm including it here.  In the new case, one can remove all copies of
the current object from the Objects window.  If you don't consider this a bug
you can close this report.

To reproduce on 6.5.80945:

Pick Current object from Objects window and drop it in empty space below.
Now there are two Current objects (the original and one copy).
Click on the top one.
Click Remove Currently Selected Object.
Now click on the remaining object.
The Remove Currently Selected Object button becomes sensitive and
   clicking on it removes the last copy of the current object in Objects window.
   It seems to me that this shouldn't be allowed.