How to completely remove a dialog on close

Why do you want to remove it?

If it is to prevent multiple instances being created, then just use the following approach...

$('#myDialog') 
    .dialog( 
    { 
        title: 'Error', 
        close: function(event, ui) 
        { 
            $(this).dialog('close');
        } 
    }); 

And when the error occurs, you would do...

$('#myDialog').html("Ooops.");
$('#myDialog').dialog('open');

$(this).dialog('destroy').remove()

This will destroy the dialog and then remove the div that was "hosting" the dialog completely from the DOM