Yes, I believe having reliable science in movies is important. People need to be able to identify with the movies to like them, so if the science in them is unreliable, this might never happen. The science involved also needs to be understandable, which I think most movies recently have been doing a good job on.
Using reliable science in movies makes for more credible movie plots and scripts. Just as accuracy in costume and movie sets is critical for developing credible plots, so is accuracy in the depiction of science in film. In addition, realistically depicting science serves an educational function, which will only benefit society as a whole.
Movie makers have a responsibility to sell us a story. If they expect us to suspend belief enough to believe the stories they have to get the background information right. If a movie-goer spends all their time in a movie thinking about how wrong the facts are, how are they going to enjoy their theater-going experience?
Movies are almost like dreams. In the sense of story and the wide range of things can happen. Man uses hyper unrealistic jetpack to fly? So be it. He needs to go save the world. Some of this "unrealistic science" needs to be there to move the plot along. Otherwise we'll spend 30 minutes on how the mechanics work. Films that do not have the purpose to be educational do not have to be. It is essentially a world of fiction. In most cases a narrative. Not everything can be explained. That's the beauty of some things.
Movies are purely for entertainment. If movie producers take liberties with actual facts to entertain paying customers, then have at it. People are smart enough to know that when they go to see a movie what they are seeing is not necessarily based in reality. Real science has its place. Science in the movies is for entertainment.