How does Iago exploit Othello's character to achieve his own end?
Iago exploits many aspects of Othello's character to achieve his own end--making those around him as miserable as he is.
Some characteristics you might consider are the following:
(1) Othello is trusting: "He thinks men honest that but seem to be so." Othello is a good man, and because he is honest and forthright, he sees others in this way. Iago knows that Othello thinks he (Iago) is honest, and that he trusts Iago's knowledge of people.
(2) Othello is a soldier, a man of action, one who must make decisions quickly. As a soldier, he would view betrayal as one of the worst offenses. And as acting head of Cyprus, Othello would view betrayal as an act of treason. We see Iago using this characteristic when he tells Othello to let Desdemona live. This type of reverse psychology works just the way Iago had planned, making Othello even more determined to kill her.
(3) Othello is also a man of absolutes. He either loves or he hates. He is not lukewarm. As he says about himself: "Away at once with love or jealousy." Othello's definition of love requires absolute trust. He cannot simultaneously love and be jealous or suspicious. So, Iago knows that if he can plant any doubt in Othello's mind about Desdemona's infidelity, he will succeed.
(4) Othello is somewhat insecure about matters of the heart. While he is excellent as a military man, in domestic matters he is somewhat ill at ease. Even in act one, Othello apologizes for his speech: "Rude am I in speech and have not those soft parts of conversation that chamberers have." Iago points out that Cassio is young, a courtier, "framed to make women false" -- in many ways Othello's opposite.