Updating a textarea label with the number of characters inside the field itself
Just a few things I notice, prolly not warranting a "mark as answer" but may help:


Cache $(this): var $this = $(this); So that you don't keep inefficiently re-wrapping this
$(this).attr('id') - really? You can just use this.id, you know. 
hasDigit === digit, so why do you have both? Scrap one of those regexes, the other one is redundant. 
Cache label.html() so that you don't keep grabbing it (which is quite inefficient). Instead: var labelHtml = label.html() and then reuse labelHtml