show 10 most recent custom post types excluding the one(s) from specific custom taxonomy

Question

Firstly, your tax query is a little jumbled. The first nested array should actually be at the ‘root’ of your query_posts() argument, with tax_query as a key among them;

array(
    'post_type' => 'review',
    'post_status' => 'publish',
    'posts_per_page' => 10,
    'tax_query' => array(
        'relation' => 'AND',
        array(
            'taxonomy' => 'reviewcats',
            'terms' => array( 'featured' ),
            'field' => 'slug',
            'operator' => 'NOT IN',
        )
    )
);

However, forgive me if I’m mistaken, but I think your query could be a lot simpler – simply exclude the ‘featured’ review you’ve just grabbed;

query_posts( array(
    'post_type' => 'review',
    'post_status' => 'publish',
    'post__not_in' => array( $post->ID ) // $post *should* be the featured review, since it was the last post queried/worked on 
) );