Factual error: In the wedding scene at the beginning, the new Mrs. Weston is shown wearing a white dress. This was not the convention at that time; white wedding dresses were pioneered by Queen Victoria (1840-1901). The bride would simply have worn her best dress.
Suggested correction: A white dress may very well have been an unmarried lady's best dress at the time, as it was common for young ladies to wear white.
Factual error: When Emma painted the portrait of Harriet, the paper was stuck to the drawing board with tape. Emma is set in 1815, but sticky tape wasn't invented until 1845.