I think I'm able to recreate this issue now. It turns out I can also no longer view/delete/edit any news item that was using the old categories that were deleted.
Follow these steps to recreate the issue:
1. Create a category
2. Create another category that is a subcategory of the first
3. Create a news item and assign it to the child category.
4. Delete the super-cat that you created in step #1 above (but do not check the child category).
The result is this:
1. Both the supercategory and the subcategory disappear from the categories module.
2. Any news item that was linked to the subcategory is now corrupted in the admin backend (you can no longer view/delete/edit that news item).
3. I believe this also caused my issue when dragging/dropping the category widget onto any page. The category widget itself appears to be corrupted.
I see on the sitefinity 4.1 discussion
that a similar bug was fixed with the 4.1 upgrade:
Content & Classifications
Fixed: Deleting category with associated images results in error in Image Administration
Is anyone able to follow the steps above (you may risk corrupting your categories) and tell me if this issue is fixed in sitefinity 4.1?
Thanks in advance for all your help,