Detect if dropdown navigation would go off screen and reposition it

I think you were almost there…

You should really only be interested in the calculations involved in the width. If the width of the dropdown element and the offset of that element is greater than the width of the container, you want to switch your menu.

$(function () {
    $(".dropdown li").on('mouseenter mouseleave', function (e) {
        if ($('ul', this).length) {
            var elm = $('ul:first', this);
            var off = elm.offset();
            var l = off.left;
            var w = elm.width();
            var docH = $(".container").height();
            var docW = $(".container").width();

            var isEntirelyVisible = (l + w <= docW);

            if (!isEntirelyVisible) {
                $(this).addClass('edge');
            } else {
                $(this).removeClass('edge');
            }
        }
    });
});

http://jsfiddle.net/G7qfq/582/