wpdb->update error

I’m not sure why you are using the the_date() function, but if you must, make sure it returns the value instead of echo-ing it.

So instead of this part:

 array( 
     'value' => the_date('Y-m-d')
 ), 

try this one:

array( 
    'value' => the_date( 'Y-m-d', $before="", $after="", $echo = 0 );
), 

To catch the update error, check out this question: Showing errors with $wpdb update

In general also remember to activate WP_DEBUG on your test site: Debugging in wordPress.