Solely because of the "I like to watch" scene, Laurence Olivier turned down the role of Ben Rand, the role which eventual choice Melvyn Douglas won a Supporting Actor Oscar for.
At one point in the mid-'70s, it was announced that Gore Vidal was going to write the screenplay.
The filming script's ending was significantly different than what was ultimately conceived and used. Eve follows Chance after he wanders away and they head back together. He leaves his umbrella behind to shield a small tree — that would have been the highly symbolic final shot. This ending was shot, and a publicity still from the press kit was drawn from it, but the actual scene didn't surface until the 2009 Blu-Ray disc.