In the opening sequence, Laurent and his friend walk the streets collecting money for charity. Laurent's friend's socks are pushed down, but when they decide to "try somewhere else," the shot of the two walking away shows the socks pulled up. In the next shot, they're down again.
During the chess match, the boys are sitting on what should be the spectator sides of the board, rather than the player sides. It appears that the chessmen were set up along the files rather than the ranks. (The lower right hand corner squares are black, when they should be white.)
Early in the movie, Clara states that she saw The Barefoot Contessa in Paris. During this early part of the movie, the French are fighting the war in Indochina. The final battle of that war, Dien Bien Phu, occurred on May 7, 1954, 4 1/2 months before The Barefoot Contessa was released. In addition, Bastille Day is celebrated on July 14th, also before the movie was released.