Question: What did the women of Sex And The City not know how to do
that Bogart and Bergman finally got right in Casablanca? 

Answer: The correct way to hold stemware! In a number of scenes throughout the series, the sophisticated ladies of Sex and the City are seen holding their wine or champagne glasses incorrectly--by the bowl instead of the stem. And, although Bogie and Bergman fumbled their goblets, as well, in Casablanca, they finally got it right in the scene where they are together for the last time in Paris. Toasting each other with champagne and holding their glasses correctly by the stems, Bogie utters one of his most famous lines: “Here’s looking at you, kid.”