While hiding out in London, Lydia hums a few bars of music. The melody is clearly from the song "My Grandfather's Clock", which was written in 1876 by Henry Clay Work, decades after the events pictured.
As they are arriving at Lydia's marriage, there are two men driving the carriage. One begins to get off to help them out of the carriage and then in the next shot they are being helped out of the carriage by Mr. Gardner. In the final shot in the scene there is only one driver - and no other in sight.
When Lizzy reads the first letter from her sister whilst staying the inn Jane writes that her nephews and nieces are wearing her out. The children in question belong to their aunt and uncle making them cousins, not nephews and nieces. None of the five sisters have any children so there cannot be any other relations for her to mention.