Much is made in this adaptation of the evils of slavery. This is resolved in the final scene with Sir Thomas Bertram divesting from Antigua and investing in tobacco. Yet in 1806, when the film is set, tobacco depended on slaves.
Fanny's armpits are clean shaven, something unheard of back in the early 1800s.
When Fanny is undressing after being caught in the rain, she undoes her corset by unhooking a metal busk at the front, this style of busk was not invented until the mid 19th century, and the film is set in 1806. Her busk instead should have been wooden or whalebone, and if it unfastened in front it would have been laced.
The harp that Mary Crawford is playing is a double action harp. The double action harp was not invented until 1810, while the movie took place in 1806.
The music we hear does not correspond to the fingering of the harp. In particular, the lowest notes should sound from the longest strings, i.e. furthest away from the player, not as shown.