Why do my custom post types show up in the dashboard, but not on my site?

flush_rewrite_rules() as soon as you register the custom post type. It appears that they have not been rewritten yet, that is, most probably, why you’re getting an embarrassing message.

register_post_type( 'mysite_reviews',
        array(  
            'labels' => array(  
                'name' => __( 'Reviews' ),
                'singular_name' => __( 'Review' )
            ),  
        'public' => true,  
        'menu_position' => 5,  
        'rewrite' => array('slug' => 'reviews')
    )
);
flush_rewrite_rules(); // <- do this only once!

Alternatively you can go to Settings -> Permalinks -> Save changes, which calls on flush_rewrite_rules() for you.

In fact http://gointrigue.com/vanilla/?post_type=mysite_reviews shows your post, which means that it’s just not being rewritten due to the lack of the proper rules, which have not yet been flushed to the database.