I'm sure there's lots of examples, but in the documentary world, The Thin Blue Line was about a man wrongfully accused of murder on death row, who was retried and released as a direct result of the movie.
Also, I think Triumph of the Will played a huge part in helping Hitler come to power. And in the US, The Birth of a Nation helped the KKK explode in popularity. These aren't particularly uplifting examples, but I think it's clear that a popular movie can have a huge effect on the political landscape.
Similarly (but less directly), the sympathetic treatment given in the 2011 Richard Linklater film "Bernie" is believed by some to have been instrumental in the release of a convicted murderer from his life sentence.
Yeah my bad, I remembered wrong. Maybe it helped cement his power? We definitely talked about this in some history class I took, but I can't find any good references online, so maybe that's a bad example.