When Darcy first introduces his sister to Elizabeth, the position of his hands changes between shots as he's telling Elizabeth that Bingley is around and wishes to meet her too.
When Elizabeth receives her two letters from Jane in the Inn at Lambton, she puts the incorrectly address letter on top of the second in her hand, but then after her uncle and aunt have left for the church, flips them again so "actually" opens the second letter as if it were the first.
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.
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.
Bingley's praise "Absolutely marvelous" for Lizzy's recital at Pemberley is out of sync.
In her letter to Elizabeth, Jane refers to being busy with her nephews and nieces. As they are her mother's brother's children, they would be her cousins.