Take a look at example 3 on this page:
It covers how to validate all the parts of the address field. This section is key:
//address failed validation because of a required item not being filled out
//do custom validation
$street = rgar( $value, $field->id . '.1' );
$street2 = rgar( $value, $field->id . '.2' );
$city = rgar( $value, $field->id . '.3' );
$state = rgar( $value, $field->id . '.4' );
$zip = rgar( $value, $field->id . '.5' );
$country = rgar( $value, $field->id . '.6' );
//check to see if the values you care about are filled out
if ( empty( $street ) || empty( $city ) || empty( $state ) ) {