I found your problem: You are using an "click" after you have already "stopped" the click event on selectable. You cannot click after it has stopped a selectable click. If you comment out the click, as below, then it fixes your main problem. Then, you need to change your selectors from "ul li div" to ".list li" because you are not selecting from your "list".
stop: function () {
var result = $("#select-result");
//$(".list li").click(function () { -----------PROBLEM-----------
var index = $(".list li").index(this); //Changed to .list li
var listLiText = $(".list li").eq(index).text(); //Changed to .list li
var listLiID = $(".list li").eq(index).attr('id'); //Changed to .list li
$(".list li").eq(index).css('background-color', '#669966'); //Changed to .list li
$(".list li").eq(index).css('color', '#FFFFFF'); //Changed to .list li
if ($("#select-result #" + listLiID).length == 0) {
result.append('<li id="' + listLiID + '">' + listLiText + '</li>');
}
sortColumns();
//});
}
Your updated JS Fiddle: http://jsfiddle.net/NkgC2/30/