Deliberate mistake: In the scene where Marie is trying on shoes, a pair of powder blue high top Converse sneakers can be seen next to her feet. It must have been done intentionally, but since there is no trace of modern apparel anywhere else in the film (the closest would be the mere mention of hot pink dress fabric but, as it's not shown, we don't know what exactly Marie calls "hot pink") these shoes (and the fabric) can't be considered part of a thematic element or artistic license.
Factual error: Marie Antoinette has moved into her new vacation home following the birth of her daughter. Her friends are visiting, she is walking through the field of wildflowers, and she blows a ladybug off her finger. The camera pans upward to show her gazing at the sky. There is a very obvious vapor-trail from a large airliner cutting through the center of the camera shot, from one side of the screen to the opposite, predating jet-liners by over 150 years.
Continuity mistake: In the last scene, inside the coach, Marie Antoinette looks out the window at the palace garden. Louis asks if she's admiring her new lemon tree avenue; she answers she's only saying goodbye. If you look at the view of the window when Louis asks the question, you can see half of the fountain and the lemon tree avenue quite close. Next frame, when Marie answers, you can see almost the whole fountain and the lemon tree avenue quite far from where the coach is.
Continuity mistake: At the beginning, when Marie Antoinette gets into the carriage she is on the left side, but when the camera focuses on her again she is sitting on the right side. Also, she is wearing a blue dress when she arrives at the tent, but when she gets out of the carriage her dress is white.