The kitchen cupboard where Rory takes her coffee mug switches between being open and closed throughout the opening scene.
During the opening scene Rory picks up a coffee mug, gripping the body of the mug. In the next shot, however, she is holding it by the handle, quicker than she would be able to switch grips.
When Paris asks Logan why he is now living with her, Rory, and Doyle, he says that he no longer has his apartment since he no longer works for his father's company. Logan, however, has two apartments. At the end of the sixth season (Partings (2006) ), Logan told Rory that he had paid rent on the first apartment for the next year, so she could stay there while he was in London. Even if Logan lost his new apartment in Manhattan, they should still have access to the New Haven apartment until approximately June.