See Customize Firefox controls, buttons and toolbars article

Firefox 4+ versions have two bookmark buttons with a star in the Customize window.
One star button has a drop marker that open a Bookmark menu.
The other star button without the drop marker opens the bookmarks in the sidebar.

You can drag the Bookmarks menu button with the drop marker in the Customize window from the toolbar palette on a toolbar (e.g. Navigation Toolbar or Tab Bar or to the left side of the Bookmarks Menu Items).

• http://kb.mozillazine.org/Toolbar_customization

Sorry apparently I wasn't clear enough.

My default tool-set does not show a second bookmark button with the drop down option.

Only one bookmark button is available - the one which makes a sidebar.

EDIT: Also restoring the default set does not resolve this issue.

You only see the Bookmarks Menu button if the Menu bar is hidden (View > Toolbars or Firefox > Options).
If the Bookmarks Toolbar is visible then the Bookmarks Menu button is displayed on the Bookmarks Toolbar as part of the Bookmarks Toolbar Items (bookmarks).
Otherwise the Bookmarks Menu button will appear on the right side of the Navigation Toolbar.

See also:

• http://kb.mozillazine.org/Corrupt_localstore.rdf

Ah ha! Hiding the Menu Bar did indeed fix my problem. I guess there's not supposed to be a drop down button in the tool-set.

Thanks for the replies.