Continuity mistake: At Molly's party after returning from Europe, the Duchess is introduced, and everyone bows. The shot shows Molly reaching for her neighbor who's standing straight, to bow down, and she does. Then there is a long shot showing the crowd, and the neighbor is again standing, and then you see Molly reach out for her again as she just had.
Other mistake: Johnny Brown is serenading Molly in the meadow as she sits up on the branch of a tree. In shots where we are looking down on Johnny (from over Molly's shoulder), the shadow of the canopy that protects the actors from the sun can be seen as a perfectly straight line on the ground, behind Johnny. The shaded/unshaded areas move as the canopy shifts in the breeze.