There are two schools of thought with regard to "poetic justice" in Shakespeare's Othello.
Early on, "poetic justice" was a literary device, which required...
...in literature, [that] good should be rewarded and evil punished.
Early critics of Shakespeare's works took this definition seriously, and found Shakespeare wanting.
The burden of the critics from Rymer to Johnson was that Shakespeare had violated all our fundamental notions of "poetic justice," or in other words had paid no attention whatsoever to moral considerations.
Shakespeare was austerely judged by some because he had not addressed these criteria in Othello: Desdemona is a loving and loyal wife. She should be rewarded based on this definition, but is punished. While Iago is unquestionably evil (and is punished), Othello is more a tragic than evil man. Even so, based on the definition, Othello is not good; so in killing his wife, he, too, is evil and should be punished. Because Shakespeare did not follow these guidelines, his work garnered some criticism.
However, Percy Bysshe Shelley, who was a fine Romantic writer in his own right, studied the works of Shakespeare, including Othello, looking for a clearer way to interpret the play. He did not see Othello as a villain at all:
...in Othello Shakespeare was portraying a man whose misfortunes were due to the intrigue of another, and were not intended by the dramatist to appear as retribution for any of his own misdeeds.
For those who find Othello an evil man on par with Iago, Othello's murder of his loving wife denotes evil, and therefore he should have received the same punishment as Iago for poetic justice to be served.
However, for those who are in agreement with Shelley, Othello is not punished because he is not evil. He is Iago's victim. However, he is still a tragic hero, and he does die (by committing suicide) at the story's end.