Is it possible to use jQuery's modal dialog instead of the browser-standard alert when using ajax_command_alert()?
I solved this problem in two ways - first, I added my own JS file which adds a modal option to Drupal's AJAX commands with the following JS code:

jQuery(function() {

    // Add modal dialog option to Drupal AJAX
    Drupal.ajax.prototype.commands.modal = function(ajax, response, status) {
        // Code to create a modal dialog goes here
    }   

});


Then, in my AJAX callback on the server, I used the following code:

function feedback_form_submit($form, &amp;$form_state) {
    return array(
        '#type' =&gt; 'ajax', 
        '#commands' =&gt; array(
            array(
                'command' =&gt; 'modal',
                'text' =&gt; "Form submission successful!"
            )
        )
    );
}