Scenes showing Cole Porter musicals being produced on Broadway in the 1930s show African-American and white women dancing together in the chorus lines. Broadway chorus lines weren't racially integrated until the 1970s.
When the Porter's are getting married, right after they are announced, all their friends and family come over. Someone comes over and gives Linda a kiss on her right cheek, which then leaves a mark. Not long after, the mark is gone, with no sign of Linda wiping it off.
When Cole Porter is in the garden playing his piano and Linda comes back from being away, Cole stands and talks to her, and the cushion on the back of the chair falls down. As he sits down, the cushion is back in place.
The scene depicting the song "So In Love" on the opening night of "Kiss Me, Kate" depicts the song as a duet between the two leads during the show's Shakespearean play-within-a-play. In "Kiss Me, Kate," "So In Love" is not a duet. Both of the leads do sing solo versions of the song at a different point in the show, however neither takes place in the play-within-a-play.