After meeting Isabelle and Theo, and spending all night with them, Matthew gets back to his hotel room. In the meantime, it starts raining so the three of them cover themselves with Matthew's coat, but when he gets to his room and leaves the coat on the bed, it is perfectly dry.
Early in the film, Matthew hides a stolen photograph of Isabelle in his underpants to prevent his hosts from seeing him with it. Later, he loses a contest with Isabelle and is forced by her to strip and the photograph is still inexplicably in his underwear, even though several days have passed and he is wearing completely different clothes.
On the walk along the canal, Isabelle states that she "...entered this world on the Champs-Elysees, 1959." She is obviously much older than 9, but she is not referring to her actual birth. She is reciting a speech from Breathless, whose clips are shown.
At the end of the movie, Theo and Isabelle's parents come back to the house and start to whisper to each other in perfect English instead of French. However, as the mother is English (which Isabelle told Matthew when they first met), it should not be surprising that they would converse in English.