Imagine watching a detective film or TV show where an interface like Project Natal allowed you to shift objects within the scene. While the characters are talking or doing whatever, you can use virtual hands to pick up things to look underneath, or push things aside to look behind them -- do your own sleuthing.
Imagine having limited control of the camera angle so you see what's happening behind or above the characters. You could peak around corners before the character does... but can't warn him or her of the danger.
Or imagine being able to change the setting in ways that the characters can interact with. Perhaps you steal the investigator's mug of coffee, and he looks around for a few seconds in puzzlement. Or perhaps you stack a lot of boxes just behind the character so, when he turns around, she bumps them and they collapse on top of her.
All of these examples have problems. For example, in the first scenario, what happens when the detective looks at an object which you've just moved and carries on his conversation as if nothing changed? I'm proposing these examples just to show there is much untapped potential for the blending of films and interaction.
It could be more game-oriented, making the audience's interaction vital to the plot. A mystery story might not be solved unless the player finds and points out clues while the detective is on the scene. Think of it as a real-time mystery game, where the player does not have all day to find clues. The player might even have to point out facial expressions on witnesses during interrogations for the detective to notice and respond.
Or it could be basically a film with view-only interaction, as in my second example.
It's one of the great wonders of life that we never run out of room for discovery and innovation. This is one area where I'd like to see more.