Millie's beads have a mind of their own. They do not stay in place even when she is standing still. Besides the funny scene during the title credits (when it is deliberate), and when Miss Dorothy registers, they also move during a scene when Millie displays her thoughts on Miss Dorothy's beads when the two of them go into the elevator for the first time.
During the title sequence, as Millie is buying a pack of cigarettes from a vendor her undergarment breaks, the vendor stares at her in surprise, and she does a slight curtsy and walks away. When the film was originally released, that was followed by a quick shot of the vendor looking down and seeing Millie's broken undergarment lying on the sidewalk, but for some unknown reason that shot has been deleted, at least from the version on VHS and the one shown on TV. (I don't know whether it is included on DVD.).