custom field in admin columns

Try replacing everything from the comment downwards with this. Basically you seemed to have a function in there that wasn’t getting called, and you need to add the case "incr_number" test to the woo_supportpress_ticket_custom_columns function:

/*-----------------------------------------------------------------------------------*/
/* Admin columns for post types */
/*-----------------------------------------------------------------------------------*/

function woo_supportpress_ticket_columns( $old_columns ){

    $columns = array(
        'cb'          => '<input type=\"checkbox\" />',
        'title'       => __('Ticket Title', 'woothemes'),
        'incr_number' => __('Ticket ID', 'woothemes'),
        'status'      => __('Status', 'woothemes'),
        'priority'    => __('Priority', 'woothemes'),
        'type'        => __('Type', 'woothemes'),
        'author'      => __('Submitted by', 'woothemes'),
        'assigned'    => __('Assigned to', 'woothemes'),
        'comments'    => $old_columns["comments"],
        'date'        => __('Date', 'woothemes'),
        );

    return $columns;

}

add_filter('manage_edit-ticket_columns', 'woo_supportpress_ticket_columns');

function woo_supportpress_ticket_custom_columns( $column ) {

    global $post;

    $ticket_details = woo_supportpress_get_ticket_details( $post->ID );

    switch ($column) {
        case "incr_number" :
            echo get_post_meta( $post->ID, 'incr_number', true );
        break;
        case "status" :
            echo get_the_term_list($post->ID, 'ticket_status', '', ', ','');
        break;
        case "priority" :
            echo get_the_term_list($post->ID, 'ticket_priority', '', ', ','');
        break;
        case "type" :
            echo get_the_term_list($post->ID, 'ticket_type', '', ', ','');
        break;
        case "assigned" :
            if ($ticket_details['assigned_to']->ID>0) :
                $link = get_author_posts_url( $ticket_details['assigned_to']->ID );
            else :
                $link = add_query_arg('assigned_to', '0', get_post_type_archive_link('ticket'));
            endif;
            echo '<a href="'.$link.'">'.$ticket_details['assigned_to']->display_name.'</a>';
        break;
        case "id" :
            echo '#'.$post->ID;
        break;
    }
}

add_action('manage_ticket_posts_custom_column', 'woo_supportpress_ticket_custom_columns', 2);