WP_LINK_PAGES Generating Unnecessary </p> Tag

Question

This is the current output for my WP_LINK_PAGES, notice the unnecessary </p> tag at the end.

My code for my custom WP_LINK_PAGES can be found here.

<div id="link_wrap"> <span class="classlinks">1</span> <a href="http://themeforward.com/demo2/?p=1948&#038;page=2"><span class="classlinks">2</span></a> <a href="http://themeforward.com/demo2/?p=1948&#038;page=3"><span class="classlinks">3</span></a> <a href="http://themeforward.com/demo2/?p=1948&#038;page=4"><span class="classlinks">4</span></a> <a href="http://themeforward.com/demo2/?p=1948&#038;page=2"><span class="classlinks">Next page</a></div>
</p>

Answer 1

the </p> is just a browser artefact to compensate for a missing </span>;

your code is missing . $args['link_after'] in two locations;

the corrected code:

// WP_LINK_PAGES: Add prev and next links to a numbered link list 
add_filter('wp_link_pages_args', 'wp_link_pages_args_prevnext_add'); 

function wp_link_pages_args_prevnext_add($args) { 
    global $page, $numpages, $more, $pagenow; 
    $args['before'] = '<div id="link_wrap">'; 
    $args['after'] = '</div>'; 
    $args['link_before'] = '<span class="classlinks">'; 
    $args['link_after'] = '</span>'; 
    if($page-1) // there is a previous page 
        $args['before'] .= ' '. _wp_link_page($page-1) . $args['link_before'] . $args['previouspagelink'] . $args['link_after'] . '</a>' . ' ' ; 
    if ($page<$numpages) // there is a next page 
        $args['after'] = ' '. _wp_link_page($page+1) . $args['link_before'] . $args['nextpagelink'] . $args['link_after'] . '</a></div>' ; 
    return $args; 
}