Don Pedro is most noted for his regal graciousness. He is titled Prince of Arragon and his demeanor is befitting that of a prince in his interactions with his subordinates and with his host and his host's family. He willingly awards honor to his deserving soldiers and willingly speaks with them as equals such as in the conversation between Claudio, Benedick and himself. Further he willingly helps Claudio win Hero's love and hand in marriage, even to the point of impersonating Claudio who is tongue-tied by his emotions for Hero.
However, when presented with what would be a great infamy and religious sin--the prospect of Hero being unfaithful to Claudio--he agrees rather quickly with the shocked Claudio that, if the accusations prove true, Hero should be publicly denounced instead of quietly rejected. Further, when presented with what seems like irrefutable evidence against Hero, he rather quickly believes what is seen as shadows at a distance, with the strongest evidence being a bedroom window, rather than pursue a deeper investigation and attain cold hard facts in the form of visual confirmation of the shadowy form being Hero's person. After Hero has been denounced, Don Pedro shows his lofty side and unrelentingly exposes what he believes to be Hero's infamous behavior.
A portrayal of Don Pedro would include all three of these character facets--facets that make him a well-rounded, multi-dimensional character--each of which is underpinned by his royal status as Prince of Arragon. Don Pedro is regal and gracious. He is able to punish immorality and dishonor. He is able to stand his ground in the face of opposition. His error (if this were a tragedy, it would be his fatal error) is his quickness to take up arms, so to speak, against that which violates the morality and honor. Had he tempered Claudio's impetuousness and seasoned it with a prince's mercy and had he challenged Don John's accusations and insisted on firm evidence instead of shadowy suggestion, then Hero would not have been devastated and he and Claudio would not have played the fool's part at Don John's malicious manipulation of events.