The Sound Engineer actually swallowed a microphone and recorded the inner audio of his body in order to achieve certain similar sounds for the film.
Willem Dafoe was ready to go fully naked for the sex scenes. But after Lars von Trier and other crew members saw him undressed, they discovered that Dafoe was too well endowed. Von Trier figured that this would distract the audience, which led to the decision to use a body double for those scenes.
When the filming started, Lars von Trier had just left a mental hospital where he stayed for two months, receiving treatment for depression. He had not completely recovered at the time and was even unable to operate the camera as he usually does, which made him very frustrated. He repeatedly excused himself to the actors for being in the mental condition he was, but, according to him, the actors supported him and throughout production, he did not experience any grave problems, except for his own condition.
First part of the "Trilogy of Depression" also including Melancholia (2011) and Nymphomaniac: Vol. I (2013) / Nymphomaniac: Vol. II (2013).
Lars von Trier's "Trilogy of Depression" contains extensive homages to the works of Russian filmmaker Andrei Tarkovsky. This film features a scene with Willem Dafoe standing quietly in the rain, surrounded by lush scenery, a clear reference to the opening scene of Solaris (1972).
Lars von Trier: [Hypnosis] On the train prior to entering Eden, 'She' is hypnotized by 'He' as part of her therapy.