Kirsten Dunst worked very hard to learn the piano piece she plays on-screen. She had originally mastered two musical pieces, but one was cut from the final release, much to her chagrin.
Kirsten Dunst and Benedict Cumberbatch were so into their characters that they did not speak to each other during filming.
For this film, Jesse Plemons and Kirsten Dunst became the fourth married couple nominated for Academy Awards for performing in the same film, after:
Kodi Smit-McPhee suffered from a severe cataract in one of his eyes during a lot of the filming. (The actor is already blind in one eye.)
At the start of filming, Dame Jane Campion introduced Benedict Cumberbatch to the cast and crew by saying "This is Phil. You're going to be working with him. Benedict is really nice but you're not going to meet him until the end of the shoot".