Corrected entry: In Madeleine's suicide attempt scene, the plot line gives us to understand that she drove herself to San Francisco Bay alone in her own car before jumping in. After Scottie rescues her, he places her, unconscious, into his car and takes her to his apartment. She awakens some time later, and during a telephone call between Scottie and Elster, she dresses and gets into her car and leaves the scene. There is no explanation of how her car got from the suicide attempt location to Scottie's apartment. She could have taken a taxi or thumbed a ride, but she did neither, since she is shown driving away in her own car.
Corrected entry: How does it happen that Madeleine/Judy is able to enter the McKittrick Hotel unnoticed by the manager, and leave unnoticed by either Scottie or the manager? So far as I could tell this was not explained by the fact we subsequently learn that she was an actress posing as Madeleine, as there should in any case have been someone in the room when they checked, and her car can't have got away on its own.