All valid questions. I left out some of that junk cause I wanted to keep it simple, but basically what happens is the delete link has a bound action (courtesy of jQuery). Click the link causes it to display a dialog box that asks if you are sure. If you say yes, then the action function gets called. 

As for the population of the attachments list, I though since it was a rerender and its variable is the attachments list, the method getAttachments would be invoked again and now that list would be minus the attachment that was just deleted. There is a method called getAttachments that looks like this.

   // retrieve the existing attachments
    public List<Attachment> getAttachments()
    {
        if (attachments==null)
        {
            attachments=[select Id, ParentId, Name, Description from Attachment where parentId=:sobjId];
        }
        
        return attachments;
    }

 I also tried hard coding a call to getAttachments within my delete function, but it didn't seem to make a difference. You might be onto something though. The list may be rerendering, but the list is still the same. Any ideas for an easy test to see if the table is actually getting redrawn?

Also, other code that I mentioned.

Registering the action of the delete link

          $('.deleteLink').click(function() {
                 id = $(this).attr('id');
       
                 $('#dialog-confirm').dialog('open');
                 return false;
           })

Creating the dialog that lets users confirm they want to delete the file

            $( ".dialog" ).dialog({
                resizable: false,
                autoOpen:false,
                height:140,
                modal: true,
                buttons: {
                    "Delete File": function() {
                     
                        $( this ).dialog( "close" );
                        removeAttachment(id);
                        
                    },
                    Cancel: function() {
                        $( this ).dialog( "close" );
                    }
                }
            });

 
the div used for the dialog box

<div id="dialog-confirm" class="dialog" title="Delete Attachment?">
    <p><span class="ui-icon ui-icon-alert" style="float:left; margin:0 7px 20px 0;"></span>Are you sure you want to delete this attachment?</p>
</div>