There were [a] couple of things I noted down during the show.

noted 是动词 note 的过去式，note 的意思是"记录、注意"。 down 是副词，在这里与 note 搭配使用，表示"写下、记下"的意思。 noted down 是一个短语动词，意思是"记录下来、写下来"。