The first type of moral reasoning introduced is a need to be responsible. This is voiced by Henry Fonda's character, but also the jury foreman (and some of those who vote guilty early on). All those characters are doing what they think they must.
Closely related is the sense of duty to the community. Though duty seems weak in the juror with the tickets to the baseball game and the advertising man, all feel duty sufficiently to play their roles in the system.
Faith in the system is a kind of moral reasoning, and it is articulated by both Fonda and by the angriest of those claiming guilt for the accused. Fonda's character thinks that they should spend full time as the system intended uncovering guilt or innocence; the angry jurors trust that the system has worked as it should.
Fairness is called for, a kind of moral reasoning, but also circumstantial reasoning and situational ethics, when various men try to discuss how his origins would affect the accused.