In the dining scene (42:05) Jesse (Ethan Hawke) and Anna (Ariane Labed) are shown side by side, but just after a shot (42:23) they are sitting away from each other.
At the airport, the same extra in a purple dress passes Jessie and his son twice in successive shots.
Jesse's hair style changed when he and Celine are in the hotel room. The hair style is back to the previous style again when they sit outside.
While Jesse and Céline are walking on the stony path, Céline's hair moves in between shots.
While Jesse and Céline walk along the stony path (where they see the goats) a man passes them; but his timing is off as it takes him too long to pass in one shot and then to the other.
When Jesse and Celine are watching the sunset, there is no sunlight on their faces.
During dinner Ariadni is taking photos of Celine and Jesse and we can hear two snaps of the shutter in a row but the camera is a Leica M6, which has to be wound on after each shot.
When Jesse and Céline are in the hotel room arguing at a table, the camera operator is reflected in the framed picture on the wall.
Jesse doesn't calculate their ages correctly. During the walk to the hotel, they discuss that Jesse is now 41 years old. A few minutes later Celine calculates that they have to be together another 56 years to match Jesse's grandparents relationship, and Jesse states they will be 98 years old by then. 56 plus 41 is 97, not 98.