They show movies almost every day, usually in the Vista Lounge (bring a sweater) or the Princess theater. One of the movies was Moulon Rouge, also Bridget Jones Diary (?). I don't think there's a charge.
Just got off the Sea Princess on Saturday - some of the movies were Legally Blonde, Moulin Rouge, Bridget Jones' Diary, Shrek. They were shown in the theater one day and on the in room television (continously throughout the day) another day. There is no charge for movies on Princess.