Get all post attachments except featured image

$args = array(
    'post_type' => 'attachment',
    'numberposts' => null,
    'post_status' => null,
    'post_parent' => $post->ID
);
$attachments = get_posts($args);
if ($attachments) {
    foreach ($attachments as $attachment) {
        echo apply_filters('the_title', $attachment->post_title);
        the_attachment_link($attachment->ID, false);
    }
}

In the code above, theres exist a way to get:

1. All attachments links except featured image.

2. All PDF attachments links only.

I was reading:

• http://www.wprecipes.com/how-to-show-wordpress-post-attachments

• http://johnford.is/programmatically-pull-attachments-from-wordpress-posts/

For the first one, you can add 'exclude' => get_post_thumbnail_id() as a parameter (as shown here).

For the second one, you can add 'post_mime_type' => 'application/pdf', but I’m not sure that would always work, afaik, pdfs have more than one mime type.