Continuity mistake: Near the beginning, when Ethan Hawke is talking about his travels while in the lounge car ("I had a friend in Madrid"), he's got his hands clasped in front of him, then the camera cuts to the woman, and his hand is outstretched, holding a salt cellar.
Visible crew/equipment: Towards the end, when they're listening to the harpsichord, Ethan Hawke says that he's going to take her picture. Around then (in the video, at least), a boom mike drops in slightly from the top of the screen.
Factual error: When asked, Julie Delpy says the reason her English is so good is because she spent a summer in LA. Come on. Even after a year, almost no one could manage to speak and pronounce a foreign language that well, let alone in a summer. Her English is very nearly flawless. We know she has spent some time in London before, but if she had stayed there long enough to learn to speak such good English, she would have learned it the way they speak it there, which means she would have a British accent and not an American one. Someone - whether or not she's a native speaker - doesn't change accents after spending a mere three months somewhere.