As Isabelle leaves their "tent," all three are naked. When she returns and reclines with the hose, all three have robes or shirts.
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.
When Matthew returns to the room to discover Theo in bed with Isabelle, Isabelle's expression and hair keeps changing position during shots.
When Isabelle takes Matthew to see her Father, she ruffles his hair and it messes. In the next shot it's perfectly neat.
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 (1960), 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.
During the riot when Theo and Matthew join the group dispensing petrol bombs the shadow of the camera is seen on Matthew's back.