Why did Dill start crying?
During the trial, all of the children (Scout, Jem, and Dill) are exposed to the harshness of the world for the first time. Until the trial, good and evil seemed as clear as black and white, and that good always triumphed over evil. To hear adults in the courtroom yelling and arguing is enough to bring Dill to tears. The children are not used to this kind of aggression between adults.
While Dill is the only one to really visibly react to the events of the trial while in the courtroom, the aftermath of the trial has a much harder impact on Jem. Dill responds as a child responds-he hears the argument, panics, and cries. Jem, on the other hand, very strongly believes that Tom will be not be found guilty. When Tom is in fact convicted, Jem experiences heartbreak and a loss of innocence. Good has not conquered evil this time. He is no longer a naive child, and he now has to come to terms with the way the world really works. This causes him to continually lash out at Scout, who still retains her childlike innocence.