When Tommy picks up his mother's cigarettes out of the toilet, one of them very obviously breaks in half. Yet a few shots later, they are all unbroken and normal.
In the opening of the movie, David Duchovny is seen riding his bike through Paris. Apparently, in the shot where he is riding through the middle of traffic was not planned or rehearsed, he simply began riding a bicycle through heavy traffic while the camera man filmed him. He attributes this foolish choice to his "Having drank a glass of wine" earlier that night.