There are several flaws in the United States justice system exposed by Twelve Angry Men by Reginald Rose. The first appears in the title, which suggests that juries are not always representative of the ethnic and gender makeup of the country.
Next, the initial problem of the mandatory death sentence skews the debate away from a pure question of innocence or guilt. Because the death penalty is so cruel and irrevocable, many people may be unwilling to pronounce someone guilty even if there is the slightest doubt.
The next problem is that although jurors are selected randomly, that does not mean that they are all free of prejudice or able to think or analyze clearly.
A final issue is how group think and peer pressure can affect the decision making process. One charismatic character can sway people's opinions. Other people may defer to the majority simply because they are not comfortable going against their peers. At times, emotions can sway decisions.