Ah, the problem is that you have TWO input fields named “address” in your form. So when somebody unsubscribes, they fill in their email address in the bottom form. Unfortunately, since the subscribe input form is named the same thing, that is what gets passed to the add_list.cgi script, and it is blank (and therefore invalid!).
Generally people just use one input for the email address and then two buttons, subscribe and unsubscribe. You can do it your way as well, but what you’ll need to do is make two whole areas, each with all the hidden fields, but one with the subscribe button and one with the unsubscribe.