There 5 ways to save a new Bookmark in Firefox:
1. {Ctrl + D}
2. Right-click and select Bookmark this Page.
3. Bookmarks > Bookmark this Page
4. Double-click the Star that is on the right side of the Location bar.
4a. (A single-click on the Star will save the new Bookmark to the Unsorted Bookmarks folder.)
5. Left-click and drag the website image (Favicon) in the URL bar (or on the active tab) into the Sidebar view of Bookmarks {Ctrl + B}
or to the Bookmarks menu bar item (the drop-down will open) and then onto the drop-down listing of your bookmarks and folder of bookmarks (folders will open)
or onto the Bookmarks Toolbar - the new bookmark will be saved when you release the left mouse button

See if any of the other ways to save a new bookmark works on those pages.

Also if you have general problems with bookmarks, see http://kb.mozillazine.org/Locked_or_damaged_places.sqlite

Thanks in advance!

The problem is solved, thank you very much. None of the methods described here to add a bookmark worked on any page of youtube.com.

I run the Places Maintenance add-on (following these instructions) and all is functioning normally once again.