I am establishing Wordpress 3..1 for any novice user. The Dashboard icons are properly placed, and I would like these to stay this way. So far as I understand, there is no add_filter or add_action hook to avoid dragging, so another approach is always to create a wordpress plugin that utilizes jQuery to disable dragging. What handler(s) would I override -- click, mouseUp, mouseMove, etc -- as well as on which DOM elements?

Maybe the simplest factor to complete is avoid the new order from being saved. This can allow the user alter the order, however it will not save the alterations for the following time the page is loaded.

You need to avoid the meta-box-order ajax event:

add_action('check_ajax_referer', 'prevent_meta_box_order');
function prevent_meta_box_order($action)
    if ('meta-box-order' == $action /* && $wp_user == 'santa claus' */) {

You will find most likely other actions you need to prevent too. Open Firebug and look for which demands to admin-ajax.php are created whenever you do stuff that you'd like to avoid. Or hide the Screen Options tab with CSS.

Make use of a Roles wordpress plugin like WordPress › Role Scoper « WordPress Plugins to limit exactly what the user can perform. Not recommended to edit core files, as the changes can get overwritten on upgrade.