Tony Curtis stated in his 2008 autobiography that he asked 20th Century-Fox to consider him for the role of Mark Wallace but they declined and cast Albert Finney instead.
Audrey Hepburn and Albert Finney were required to "direct" themselves in several sequences where they were shown inside of a moving automobile. They pushed the camera's buttons while director Stanley Donen rode alongside them in another car.
When Mark and Joanna are riding away in the concrete pipe, you can clearly see that the truck carrying them has a large set of wheels as the furthest back portion of the truck, which would make it difficult for them to just jump out. But when they cut to the scene where they are jumping out, the large set of wheels is gone.