The most obvious answer to this question is that Tom Robinson was a black man accused of raping a white woman. This type of case was a highly unusual one for the times; in many such instances, the black man could well have been lynched before going to trial (as Tom nearly was himself). The other unusual facts are that we are led to believe that Tom is innocent of the charges; that Atticus has sufficiently proved his case; that Bob and Mayella Ewell present contradictory evidence; and that no doctor's report was made. The end result--a guilty verdict against the accused black man--is probably the least surprising fact of the trial.
As was mentioned in the previous post, Tom Robinson's case involves an African-American who is accused of assaulting and raping a white woman. In the Deep South during the 1930s, a case like Tom Robinson's would be considered high-profile. Anytime a black man is accused of harming a white person, the public is sure to make a spectacle of the event. Typically, cases involving a white person's word against a black man's are cut and dry. However, Atticus Finch is an experienced lawyer who is going to defend Tom Robinson. For the first time in Maycomb, a lawyer actually plans on defending their black client. Atticus is unlike other lawyers in that he is not prejudiced towards black people and will defend an innocent black man to the best of his ability. Also, Tom Robinson has a good reputation throughout the community and the people accusing him of rape are despicable citizens. These elements create an unusual, unique court case in the small town of Maycomb.