Throughout the film, Jane wears costumes almost 20 years ahead of the other characters. At the ball scene, she is the only one in short sleeves and an empire waist- all the others are dressed as fits the period, which is 1795. Presumably, this was to make Jane more recognizable to popular audiences more familiar with the empire style dresses her later characters wore.
Some shots of the Austen's house show a large plant of
Clematis montana (with pale pink flowers) growing up the front almost to the roof. This species was first introduced from India to England in 1805, and it would have been many years before it became generally available to gardeners. The Austen family moved from their house (to Southampton) in 1801.
At the end of the film, in a dolly shot showing Lefroy's back, Jane closes the book and puts her hands on it. Then after Lefroy begins to applaud, in the final closeup shot, she closes that book again.
Early on, Tom Lefroy encounters Jane Austen in the woods. In the ensuing conversation the shots from behind Jane looking at Tom are in sunshine (sharp shadows of trees on the ground, etc), while during those from behind Tom looking at Jane it is grey and cloudy and there is even rain spotting Tom's fashionable hat and coat.
At the stagecoach inn where Jane and Lefroy are having drinks, Jane puts down on the table a nearly full glass of wine. After a couple of cuts, the camera pulls back and she stands to leave; the glass on the table is empty, without her having touched it again.
When Jane and Tom are speaking in the woods, as she is retreating you see Tom's profile as he is turning towards her. His mouth moves in what can be discerned as words, but he actually begins to speak once the shot changes to his full face.
When Jane and Tom are walking toward the boxing match, a blond soldier dressed in a red uniform walks in front of them smiling then passes towards the fight. A couple of seconds later, Jane and Tom have barely taken a few steps and the same character is repeated but they are not saying the same things.
When Henry Austen and other British Officers are in uniform they are wearing breast plates while at dances and boxing matches. These are only worn when the officers are on duty or in battle, not for social occasions.
Two (at least) errors occur during the cricket match. When Mr. Lafroy bowls during the cricket match, he throws the ball like one would a baseball, rather than keeping his arm straight. (Actually bowling was underarm in cricket until the mid 19th century, so the film is wrong but in a different way to the comment here). When Jane hits the ball, it clearly goes beyond the boundary. She has hit for six and the batsmen would not have to run.
In the scene where Jane meets Mr. Lefroy in the woods she walking away from him on the path and you see a rather large white string at her hem. Then, she walks back up to him, says something, and walks away again and the string has disappeared.
The goof item below may give away important plot points.
At the end of the movie, Jane sees Tom LeFroy's wedding ring and then covers her bare ring finger. However, men did not wear wedding rings during that era. It did not become customary for men to wear wedding rings until the mid twentieth century.