Other mistake: When Cecil and Gloria are having their birthday celebration, before they are informed of Charlie's death, Cecil goes to the refrigerator to open a bottle of champagne. We hear the distinct pop of a cork from a bottle of sparkling wine, so we know he chose that bottle, but when he enters the living room a few seconds later, he is holding a glass of non-sparkling wine (no bubbles are visible).
Other mistake: Travers arrives in Los Angeles and is seen at the airport and the hotel a short time later with just a small suitcase and a smaller carry-on bag, yet she has far too many clothes-suits, dresses, skirts, sweaters, blouses, sleepwear, shoes, and other accessories-than could possibly fit in them. She is seen leaving L.A. with an additional suitcase, but the third one appears to be one that is just used for carrying the big Mickey Mouse stuffed toy she takes back to London.
Suggested correction: There's nothing saying that she had to have taken all those clothes with her. It's possible that she had more clothes sent on afterwards. Maybe the extra clothes belonged to the hotel/studio etc. Maybe they were rented. Who knows? Just because it's not explained, doesn't make it a mistake.