Goofs

When The Doctor is walking among Reinette's memories, you see the placement of his hands on her head change from frame to frame.

When The Doctor is trying to fix the connection from the past to the future through the fireplace, the background of the spaceship can be seen behind the flames whilst there is no connection.

When The Doctor uses the fireplace after working out who the girl is as he presses the button, the top section of marble on the mantle lift and bend slightly.

The track that allows the fireplace to spin can be seen (the tiles on the floor do not line up correctly) when The Doctor is shown leaving for the ship the final time.

Jeanne calls herself "Reinette" in 1727, whereas in actual fact, this was a nickname meaning "Little Queen" which was not given to her until 1730, when her mother took her to a fortune-teller who said she would grow to become the mistress of a king. (Reinette means "Little Queen" in French.)

There are electric light bulbs in all the chandeliers in the Palace of Versailles in the 18th century.

When one of the clockwork people is threatening Rose electric motors can be heard.

The reason everybody is always speaking English is because the TARDIS translates for them, but when The Doctor is trapped in France and all the time portals have been closed, the TARDIS would have no connection to The Doctor, but everybody is still speaking English.

The TARDIS translates the French characters' dialect to English, except for charming phrases and interjections like 'Monsieur'.

Reinette tells the Doctor that she's known him since she was seven years old, but she first met the Doctor in 1727. She would've turned six in 1727, as she were born in 1721.