What types of moral dilemmas are there? and what should they do about it?

Certainly the moral dilemma of justice and Prejudice comes into play. They are both themes but also serve as moral questions with no easy answer.

Throughout the play, we see two opposing views of justice. From 8th Juror and others, as they join, we see a perspective of justice that favors the accused and that wants most for him to have a fair shot. To 8th Juror, the boy's poor and troubled upbringing, his shoddy state-appointed defense attorney, and the juries quick near-decisive decision to convict him are all gross forms of injustice.

Another is prejudice

Looking at prejudice in a larger sense, we find that, while maybe not racially driven, many of the jurors enter the jury room with preconceived notions and irrational ideas. 3rd Juror seems to be prejudiced against the accused simply because of his age, which seems to remind him of his estranged son. An interesting example of "reverse prejudice" is 8th Juror, who is initially sympathetic to the accused, not because of the evidence, but because he pitied his poor and troubled upbringing.