Most of the characters in Othello are either subjected to unjust acts or believe themselves to be the victims of injustice at one point or another. The plot is initiated when Iago feels he has been subjected to an injustice when Othello passes him over for a promotion. While his additional complaints against Othello vary and prove rather unreliable given the nature of his character, they all involve injustice, such as Iago claiming Othello has slept with Iago's wife, Emilia.
Othello is a character obsessed with justice. When he is tricked into believing Desdemona has been untrue to him, he demands justice for her actions. However, since the allegations against Desdemona are false, Othello's sudden coldness towards and eventual murder of his wife are both unjust in every sense, especially when considering Desdemona's staunch love for her husband and horror at the thought of even considering adultery.
Even minor characters are obsessed with the idea that they are the victims of injustice. Brabantio feels Othello has stolen away his daughter and that his own daughter has betrayed him, demanding justice from the courts and then receiving none. Emilia is mistreated by her husband and stops putting up with it at the very end of the play, which leads to her death.
Ultimately, the play does not end with any of these individuals gaining justice, unless one counts Othello's suicide as justice for Desdemona. The unjust Iago, though arrested, obtains his goal in the end.