When Hilda is braiding her hair on her left side when she is in her dressing room in Melbourne, where she is in the braid changes from shot to shot.
Hilda's name in the ads reads "Madame Hilda Bouverie." In fact, she is not supposed to be married at this point in the movie, and so should have been referred to as "Mademoiselle Hilda Bouverie."
Hilda says that marriage to Sir Julian will make her a peeress. A peeress is the wife of a lord; Sir Julian is not a lord but a knight, a lower rank in the hierarchy of titles.
At about the 28 minute mark a fly can be seen on Irene Dunne's shoulder.