JavaScript/HTML web application - user interface logic
Readability - the code reads fine.  The modes concept is explained well just by reading the code, so I wouldn't worry about that.

Code style - Javascript programmers are used to passing functions around and probably wouldn't bat an eyelid at the idea of assigning different functions to a variable, but it makes more sense to me to always have the same function as the event handler, and call the action for the current mode from within it:

var bookmarkEventMapping = function(e) {
    bookmarkActions[bookmarkActions.currentMode].eventMapping(e);
};


A couple of other things I would do, out of personal preference more than anything:


store the list of modes separately, not in the bookmarkActions object
refer to the modes using references to the actual objects, as opposed to using the object property names.


If you did store the mode list separately, you could also make things cleaner by making that list the only place where information about the modes is stored and using it to generate the html, instead of having to maintain the html and the code in initModeMenu separately.