Adding a rich text editor to Excerpt

Just replace the default output. Make sure you unescape the excerpt before you send it to the editor:

add_action( 'add_meta_boxes', array ( 'T5_Richtext_Excerpt', 'switch_boxes' ) );

/**
 * Replaces the default excerpt editor with TinyMCE.
 */
class T5_Richtext_Excerpt
{
    /**
     * Replaces the meta boxes.
     *
     * @return void
     */
    public static function switch_boxes()
    {
        if ( ! post_type_supports( $GLOBALS['post']->post_type, 'excerpt' ) )
        {
            return;
        }

        remove_meta_box(
            'postexcerpt' // ID
        ,   ''            // Screen, empty to support all post types
        ,   'normal'      // Context
        );

        add_meta_box(
            'postexcerpt2'     // Reusing just 'postexcerpt' doesn't work.
        ,   __( 'Excerpt' )    // Title
        ,   array ( __CLASS__, 'show' ) // Display function
        ,   null              // Screen, we use all screens with meta boxes.
        ,   'normal'          // Context
        ,   'core'            // Priority
        );
    }

    /**
     * Output for the meta box.
     *
     * @param  object $post
     * @return void
     */
    public static function show( $post )
    {
    ?>
        <label class="screen-reader-text" for="excerpt"><?php
        _e( 'Excerpt' )
        ?></label>
        <?php
        // We use the default name, 'excerpt', so we don’t have to care about
        // saving, other filters etc.
        wp_editor(
            self::unescape( $post->post_excerpt ),
            'excerpt',
            array (
            'textarea_rows' => 15
        ,   'media_buttons' => FALSE
        ,   'teeny'         => TRUE
        ,   'tinymce'       => TRUE
            )
        );
    }

    /**
     * The excerpt is escaped usually. This breaks the HTML editor.
     *
     * @param  string $str
     * @return string
     */
    public static function unescape( $str )
    {
        return str_replace(
            array ( '&lt;', '&gt;', '&quot;', '&amp;', '&nbsp;', '&amp;nbsp;' )
        ,   array ( '<',    '>',    '"',      '&',     ' ', ' ' )
        ,   $str
        );
    }
}

Save this code in a plugin or in your theme’s functions.php.