There is a possibility you have nothing stored as unsorted bookmarks, but the other symptom: bookmarks not deleting could suggests the database is faulty. Another possibility is that something possibly some software extension or plugin is interfering.

Back up your bookmarks and keep them somewhere safe outside the firefox paths. Then try the troubleshooting, before trying to investigate fix the database. In fact it may help to actually copy all your profile and its folders and files (it includes more backups of bookmarks that may be useful later). I am suggesting trying a belts and braces approach to make sure as much information as possible is retained.
CARE restoring bookmarks overwrites the existing set!
See

• backing up and restoring bookmarks
• http://kb.mozillazine.org/Bookmarks_history_and_toolbar_buttons_not_working_-_Firefox
  (Locked or damaged places.sqlite <-- bookmarks database)
• basic troubleshooting

Try using firefox's safe mode

• do not make changes in the first options window, just click on continue
• use only the default theme
• if problems continue, then whilst still in safe mode, disable all plugins

Well John99, I have a LOT of unsorted bookmarks, and they all work fine. They are a wide-ranging lot and so it is not easy for me to suss them out into neat folders and categories. I took the stubborn bookmark that did not want to leave its snug nest and shifted it into a folder that I DO have, and then deleted it from that folder in the ordinary manner. I am grateful to you for your effort to help me in my little situation, and I thank you. tom

A possible cause is a problem with the file places.sqlite that stores the bookmarks and the history.

• http://kb.mozillazine.org/Bookmarks_history_and_toolbar_buttons_not_working_-_Firefox
• https://support.mozilla.com/kb/Bookmarks+not+saved#w_places-database-file

Hi Gandyman,

Glad things seem to have improved. You obviously sorted out the deleting of the recalcitrant bookmark.

I guess you also sorted out:

 "Further, If I <show all bookmarks> none of my unsorted bookmarks is shown. Clicking on the "unsorted bookmarks" folder gives nothing, does nothing."  

As you now mention

 "I have a LOT of unsorted bookmarks, and they all work fine." 

John99: Ah, it is the case that I have a lot of unsorted bookmarks, and they all work fine. It is also the case that when I choose the Library view, the bottom item in the leftmost column is a folder, titled "Unsorted Bookmarks" which, when clicked does nothing and shows nothing. Since I never use the Library view, I am not inconvenienced. In the odd moment when I want to do some maintenance, I use the sidebar view of my bookmarks. I apologize if my affect in this series of remarks of mine seems less than warm. I am not trying to be that way, but rather simply factual and unambiguous - perhaps with mixed results. I continue to be gratified by your replies, and thank you for them. I do thank you. tom

Its ok I am just trying to understand what the problem is that you see. The sidebar and library should be fairly similar in the content they display, and should show folders with the same names, the library view gives more information, and should help you in identifying where the bookmarks are residing.