Highlight Current Quick Launch Menu Item

1. Add a start-up script on your page

$(function () {
    $(".s4-ql li.selected").parents("li.static").find(":first-child").first().addClass("selected-menu-item");
 });

2. Take advantage of the added CSS class to highlight current menu item:

.s4-ql UL.root a.selected-menu-item {
    background-color: rgb(0,153,0);
}

Example of the highlighted menu item: