Prevent author from editing comments from others in their post

Try use the following code in your themes functions.php

// http://scribu.net/wordpress/prevent-blog-authors-from-editing-comments.html
function restrict_comment_editing( $caps, $cap, $user_id, $args ) { 
if ( 'edit_comment' == $cap ) {
        $comment = get_comment( $args[0] );

if ( $comment->user_id != $user_id )
        $caps[] = 'moderate_comments';
}

   return $caps;
}

add_filter( 'map_meta_cap', 'restrict_comment_editing', 10, 4 );