In 3:3:591-612 Iago informs Othello that he saw Cassio with Desdemona leading Othello to show his fatal flaw, jealousy, by demanding blood for the "crimes" committed.
Peripeteia
In 3:4:533 Othello vows to kill Cassio for sleeping with his wife. This is where his pride takes over and he doesn't wait to confirm this fact and only goes off of his emotions.
Anagnorisis
In 2:1:18 Othello shows his love to Desdemona in front of Iago which is playing perfectly into Iago's plan to take advantage of his unwise love.
Nemesis
In 5:2:150-153 Desdemona finally dies. This changes Othello's fate because now he is truly the villain that Iago wanted to be and the old Othello has been destroyed.
In 5:2:667-281 Emilia tells Othello that she gave the handkerchief to Iago and he realizes that Desdemona did not betray him. Therefore he killed her for nothing.
Othello had to pay for his crimes against Desdemona and Roderigo. By killing himself he gave a sort of justice to all those involved.