Aristotle defined a tragic hero as a great man (valiant, honorable, etc.) whose death is his fault—resulting from his tragic flaw, which Aristotle defines as an "error in judgment." Brutus' tragic flaw is his naiveté: he believes that Cassius and he are united in purpose, when Cassius is simply jealous of Caesar. Brutus should have more closely questioned Cassius' reasons for wanting Caesar dead. Caesar saw Cassius as a threat:
Let me have men about me that are fat,
Sleek-headed men and such as sleep a-nights.
Yon Cassius has a lean and hungry look,
He thinks too much; such men are dangerous. (I.ii.190-195)
Brutus is also unrealistic in killing Caesar—he thinks Rome will be safer, but there are many other men vying for Caesar's power—especially Mark Antony. He uses Caesar's death to seize power, and is savvy enough to realize that he can use Brutus as a scapegoat. Even when Mark Antony approaches the assassins and promises to support them in front of the Roman people, he is already planning the punishment of Brutus and the other murderers.
Woe to the hand that shed this costly blood! (III.i.278)
At his first opportunity, Antony turns the crowd against Brutus. Antony's sarcasm is evident as he answers Brutus' charges against Caesar, contradicting these same "charges" to make the crowd angry with Brutus and the others—while praising the fallen Caesar.
But Brutus says he was ambitious,
And Brutus is an honorable man.
He hath brought many captives home to Rome,
Whose ransoms did the general coffers fill.
Did this in Caesar seem ambitious?
When that the poor have cried, Caesar hath wept;
Ambition should be made of sterner stuff. (III.ii.94-100)
Brutus, an experienced soldier, too easily believes Antony.
In Othello, Othello also exercises poor judgment—found in the undeserved trust he places in Iago.
Othello, also a great solider, is promoted to the position of lieutenant over Iago. Othello elopes with the woman he loves, much to Desdemona's father's anger. Othello is busy with affairs of state—perhaps distracted—but very much in love with his new wife.
At every turn, Iago manipulates those around Othello because Iago is jealous (as is Cassius in Julius Caesar). He lies to Othello about Desdemona and Cassio. He plants false doubts and evidence. Iago preys on Othello's jealousy; and in Othello's weakened mental state, the Moor believes all of Iago's toxic lies—including that Desdemona has slept with Cassio.
Othello's mind becomes fevered and—in a passionate rage—he strangles Desdemona, only realizing just before her death that she was innocent and truly adored him...that Iago was a liar.
A guiltless death I die. (146)
O, who hath done this deed? (147)
Nobody; I myself… (148)
You heard her say herself, it was not I….
She's like a liar gone to burning hell;
'Twas I that kill'd her.(155)
O, the more angel she,
And you the blacker devil! (156-157)
She turn'd to folly, and she was a whore. (158)
Cassio did top her; ask thy husband else. (163)
If he say so, may his pernicious soul (186)
Rot half a grain a day! He lies to the heart.
There are several truths to be learned in the flaws of Othello and Brutus. First, even great men make mistakes—their judgment can be faulty. Second, one should never believe another's words to be facts—to do so may bring about unforeseen disaster. Sadly, we must question the motives of strangers.