At the beginning of Broken City, Billy Taggart is charged with murder but then walks. At the end of the film, it seems that he still has to face his crimes. Why isn't he protected by the Double Jeopardy clause in the U.S. Constitution? Does he actually not have to face his crimes at the end?
This is a mistake in the movie. Taggart is charged with the crime of murder, and it is determined during the trial that he was acting in self defense. This is an acquittal, and because of that double jeopardy would apply, and he would not be able to be charged again for the same crime, even if he stood in the courtroom and confessed to it.
Currently this concept is recognized and enforced by a vast majority of countries in the world. It's easier to list the ones that don't recognize it than the ones that do. If a trial reaches either an acquittal or a conviction, then double jeopardy attaches.