It was one of the first modern trials, with fancy showmanship by high-priced lawyers, constant media coverage and the vocal political pundits. It caught a lot of attention because of the racial issues, but also because of Simpson's fame. It polarized people on race and class. Some people were angry because he was rich and "bought" the verdict, others thought he was targeted because of his race.
I agree with Post #3. American culture obsesses on race, wealth and celebrity. OJ Simpson's case involved all of these things. It was the perfect reality show before we had reality shows.
Because of his race, wealth, and celebrity, everyone knew who Simpson was and most people were interested in what was going to happen to him. Add in the element of spousal abuse (a women's rights topic) and you had a trial that pushed just about everyone's buttons.
So this was not a trial of the century for legal reasons -- sociological reasons are what made it such a big deal.
I, too, don't know that I agree with the assessment of the trial as being that critically important. But there were some important intersecting factors that made this case different, and highlighted a number of social and legal issues we face that might justify the nickname.
First, the justice system, it is widely argued, treats the wealthy and the poor differently. As OJ Simpson was both wealthy and a member of an ethnic minority, this was a test case for that accusation. The justice system certainly has a history of bias against African-Americans, and the LAPD has a horrible reputation for the same reason. Some thought the case at least exposed both issues and brought them into specific relief.
Secondly, this was a case where a black man was accused of murdering a white woman. "Fear of the black male" involves both prejudice and stereotype, but has its roots in sociological history. Depending on your perspective, this case could have been an argument either way, in other words, some believed that he was accused because it was alleged black on white violence.
Thirdly, Simpson was a celebrity, and as celebrities often stand accused of crimes, this drew more media attention and gave the whole affair a circus-like atmosphere.
To call the O.J. Simpson trial the "Trial of the Century" employs considerable hyperbole. It was, in fact, a sensational murder, and the defendant was a famous athlete and television personality. His representation, the so called "Dream Team" of the likes of Alan Ginzberg; F. Lee Bailey, and Johnny Cothran were the best anyone could find. The sensational nature of the trial comes perhaps from three factors: First, it was televised continuously. Secondly, a dirty cop was exposed as having planted evidence. This fact alone gave the entire trial a soap opera aura. Finally, the verdict itself; which many, myself included, consider as faulty, lent itself to the publicity which the trial received. It set no legal precedent, and had no more legal significance than the Lizzie Borden trial of the 19th century.