jquery ui selectmenu scrollbar not working

You can set the max-height for the content of the selectmenu when it is opened in CSS and then it will present a scrollbar within the list of items that can be used.

ul.ui-menu { max-height: 420px !important; }

You might need to further restrict this style-change in your CSS if you are using other jQuery UI widgets that include a <ul> element with the class 'ui-menu' assigned.

A solution is given for the example "select a number" of the JQueryUI demo page:

$('select').selectmenu().selectmenu("menuWidget").css("height","200px");