The movie that immediately comes to mind is
84 Charing Cross Road starring Anthony Hopkins. It is about an author in New York who exchanges letters with a bookseller in England during a 20 year period. It's a true story. The book is a delight, too, and one I should have mentioned in the Books NOT About Copywriting thread.
Law and Order: Criminal Intent (a television show, not a movie, but I hope it's close enough) isn't at all about copywriting but I like watching how Detective Goran gets suspects to lower their defenses and confide in him and how he shows empathy. He's also great at noticing every single detail about every single thing. He says his best tool as a detective is his library card.
The older I get the more I enjoy people-watching and shows, movies and novels give me another way to do that, and help me indirectly with copywriting.
--Anita