Hi Joe F,
I'm posting this from India five years after your post of 11 Feb 2009 which I happened to see by sheer chance while Googling the net to find some material on the background of the song. TCM carried a run of the movie on TV many years ago which I had taped and watched the song again carefully. Regarding your emendation to the lyrics, in particular, to the stanza which starts with "I know a lady named Arabella Grose..", I noticed that Sheldon Leonard, who sings that verse, looks first at Spencer Tracy and then at Akim Tamiroff as he sings the phrase "you know her and you know her..." - so its clearly addressed to each of them in succession. So the emendation is not really required. I'm sure you must have managed to see the movie sometime during the intervening years - if not, I have cropped out that particular portion from the video and can mail it to you if you like (its only about 4 MB in size).
Best regards
Krishna Sundaram