When Harper Lee published "To Kill a Mockingbird" it was 1960, the beginning of a turbulent period in the history of the United States. Many changes in racial relations were in the making, much attention to injustices handed to people of the African-American race were given public attention.
Certainly, then, Harper Lee's novel of two children's learning from their father about fighting prejudices and affirming human dignity were, indeed, relevant and controversial to the time of the novel's publication. The reports of such as the Scottsboro boys in Northern Alabama are real-life accounts that parallel the treatment of Tom Robinson.
Harper Lee's novel became a model of racial tolerance; because its author herself was from Alabama, a state heatedly involved in the Civil Rights efforts, the book could not but bring attention to many of the current issues of the times, such as "Bloody Sunday," a day that many were killed on the march from Selma (an area of 57% black) to Montgomery, Alabama, as they attempted to cross the Edmund Pettus Bridge in order to go to the state's capital of Montgomery and demand voting rights.
I believe that Harper Lee only once specifically dates the time period of her novel To Kill a Mockingbird. It comes fairly late in the book, in Chapter 20, during the Tom Robinson trial when Atticus states
"There is a tendency in this year of grace, 1935..."
The reader is left to wonder about the year up until that point in the novel, although the author does give clues to the date with specific historical references and allusions.
DRACULA. Dill provides one of the first clues to the time of the story when he declares that he has seen the movie, Dracula, which was released in 1931.
DEWEY DECIMAL SYSTEM. Jem got his Deweys mixed up when he claimed that Scout's teacher was teaching the Dewey Decimal System. He was actually referring to the educational philosophies of John Dewey, whose published works were staples of the 1920s. The DDS had actually been around since the 19th century.
DIXIE HOWELL. Howell was a quarterback at the University of Alabama between 1932-1934, becoming an All American in 1934. Scout mentions finding a picture of Howell in a magazine in Chapter 11.
ADOLPH HITLER. Scout's teacher mentions the rise of Hitler in Chapter 27. He was appointed German chancellor in 1933.
ALBERT EINSTEIN. Einstein won the Nobel Prize in 1921 and is mentioned in Chapter 20.
THE NATIONAL RECOVERY ACT. President Franklin Roosevelt's statute which supported a public works program. It went into effect in 1933 and was repealed in 1935.