Filtering out the #more anchor link that gets produced by

You can filter the_content_more_link hook and remove #more-POST_ID from the link:

function wpse_51806_strip_more_link( $more_link ) {
    global $id;
    return str_replace( "#more-$id", '', $more_link );
}
add_filter( 'the_content_more_link', 'wpse_51806_strip_more_link' );

It has even been made into a plugin, if you’re more comfortable with plugins then code snippets.