Script won’t load via plugin class

The class constructor method isn’t called until your shortcode handler is (i.e. when WordPress is searching the post content for shortcodes). This is done after wp_head is called, so you’re missing the boat.

However, you don’t need to enqueue scripts on your wp_head – and doing so for shortcodes/widgets which may not be on every page is a waste. Since 3.3 you can call wp_enqueue_script inside the shortcode/widget callback, and doing so means your script is enqueued only on pages where it is absolutely needed. The script is then printed in the footer.

class AV_Slideshow{ 

function build_slideshow($slides){

    if(!$slides){$slideshow = 'No posts are selected for this slideshow.';}

        $slideshow = '<div id="slides"><div class="slides_container">';
        foreach($slides as $post_id){
            $post = get_post($post_id);
            $title = $post->post_title;
            $content = $post->post_content;

            $slideshow .= '<span>' . $title . '</span><span>' . $content . '</span>';
        }
        $slideshow .= '</div></div>';

        //Shortcode is being used, so enqueue the script:
        wp_enqueue_script('av-slideshow', get_bloginfo('stylesheet_directory') .  '/js/AV-Slideshow/av_slideshow.js', array('jquery') );

        return $slideshow;
}

}

add_shortcode( 'slideshow', array('AV_Slideshow', 'build_slideshow') );

After that slimming down, the class structure seems a bit unnecessary. But I tend to put all my plug-in’s shortcodes into one class – particularly when the shortcodes are sharing scripts/styles and I need to print JavaScript variables to the page.