I am not too sure why you feel that there are only three main themes in this play. It is clear that any work of literature opens itself to a vast number of different interpretations, and this excellent play is no exception. However, the play does suggest in principal three general themes that we can identify as follows:
1) The nature of justice.
Clearly, the play's ending shows true justice being done. What begins as apparently a clear cut case, with various jury members wanting to get home to carry on with their lives, is saved by the stubborness and persistence of Juror Eight. However, it is made evident that justice is only won after a battle that suggests the fragile nature of justice. How many other jurys would have quickly made the wrong decision to save themselves the problem of seriously debating the case?
2) The responsibility of justice.
A part of the play that it is important not to ignore is the introduction that the Judge gives to the jurors, informing them of their role and responsibility:
I urge you to deliberate honestly and thoughtfully. You are faced with a grave responsibility.
The play points towards the vital role that we all have in ensuring that true justice is enacted. The play is as much a comment upon the justice system and our social responsibility as it is an excellent, gripping drama. Concepts such as justice, which the USA is based around, are only as strong as the individuals that help support and affirm such concepts.
3) The blindness of justice.
Traditionally, justice is depicted as a blind woman, carrying a sword in one hand and scales in the other. This blindness is essential to ensure that justice is not swayed by color, creed, or religion. Of course, this is something that Juror Ten does not exhibit. Note how he characterizes the defendant whose fate is being decided:
Bright! He's a common, ignorant slob. He don't even speak good English!
Prejudice is something that represents a barrier to true justice being enacted, and this is another central theme of the play.