Help with custom post type and custom taxonomy issue with rewrites

I believe you have a problem with the arrays you’re passing to register_taxonomy. You have:

register_taxonomy( 
    'book-cats', 
     array( 'books' ), 
     array(  
        'hierarchical' => false, 
        'label' => __( 'Book Categories', 'sp-theme' ), 
        'singular_label' => __( 'Book Category', 'xxr' ), 
        'query_var' => true 
     ) 
);

It should be something like…

register_taxonomy( 
    'book_cats', 
     array( 'books' ), 
     array(  
        'hierarchical' => false, 
        'labels' = array(
            'name' => _x( 'Book Categories', 'taxonomy general name' ),
            'singular_name' => _x( 'Book Category', 'taxonomy singular name' ),
            /* etc. */
        ),
        'query_var' => true 
     ) 
);

Note that…

• Your taxonomy name has an underscore rather than a hyphen
• ‘labels’ is passed as an array rather than individual elements