When Hoover was put in charge, he insisted that agents be college-educated and clean-cut. He focused the FBI's efforts on scientific examination of crime scenes. He made crime scene investigation a scientific and rigorous endeavor. He believed, correctly as it would turn out, that scientific examination of a crime scene could lead to identification of the criminal. He collected fingerprints from around the country into a centralized database to enable better matching and identification.
The kidnapping of Charles Lindberg's baby is depicted in the film. It was the most popular crime of its time, every twist and turn followed by the entire nation. Hoover used new scientific crime-fighting technologies to help solve the crime. He matched the wood of the ladder to a particular lumbar company and he used a technique that seems obvious today but was revolutionary for it's time -- marking money that was used for a ransom payment. The marked money could be traced later when it turned up in local stores.
The movie also shows Hoover's complex personal life. Hoover fought his emotional demons about as strongly as he fought criminals. He couldn't accept that he was gay and lived his life chaste, spending most of his time with his closest friend and assistant. He had an extremely close relationship with his mother and was devastated when she died. He was also prone to taking credit for others' accomplishments and relished power and the spotlight.
There's no doubt that J. Edgar Hoover transformed the FBI, creating a world-renown and respected law enforcement organization. Its high reputation carries on today. The movie did a good job depicting his critical role in shaping the future of criminal investigation.