I would like to add a few other ideas about Othello's intelligence. First of all, Iago is able to dupe or manipulate many other charactes in the play: Roderigo, Cassio, Montano, Brabantio, Emilia, and to some extent Desdemona. So, the fact that Othello falls to his persuasion is not that surprising--he is only one of many. Further, Iago works on Othello for an entire act and part of another (Act 3 and Act 4, scene 1). It takes longer for Othello to fall under Iago's spell than any other character. Look at the persuasive techniques that Iago uses with Othello in Act 3, scene 3, and compare these to the ones he uses with Roderigo in Act 1 or Cassio in Act 2. With Roderigo, Iago only has to repeat himself: "Put money in thy purse." With Cassio, Iago only uses sympathy, reassurances, and deceptive advice. With Othello, Iago must pull out all the stops: inference, reverse psychology, imagery, deceit, ethos. Othello has known Iago much longer than he has known Desmona. As a general, Othello has trust in his men. He has no reason to doubt Iago. And Iago's seeming reluctance to tell Othello his thoughts is a powerful hook that I think almost anyone would fall for. You must remember that Othello is not privy to Iago's thoughts as we are.
Other than Othello's trust in him, Iago's most potent weapon is Othello's latent insecurity. When Iago delicately mentions his race, Othello begins to doubt Desdemona's faithfulness. Othello compares himself to Cassio with the phrases "Haply, for I am black" and "I am declined into the vale of years and have not those soft parts of conversation that chamberers have." Othello sees himself as black, older, and crude. When Othello views himself this way, he jumps to the conclusion that of course Desdemona loves Cassio: how could she possibly love Othello? Cassio is white, young, handsome, well-spoken, charming. Othello is black, older, and lacks courtly speech.
This type of doubt plagues many relationships and is most probably the root of most jealousy. It is our own insecurities that make us jealous. It is when we compare ourselves to others and find ourselves coming up short that we begin to doubt whether or not we can be truly loved by another. This mindset has nothing to do with intelligence; it has everything to do with our estimate of ourselves.
Othello's leap to murder his wife seems extreme to us, and probably foolish. But Othello, a soldier, is a man of action. In his mind, Desdemona and Cassio have committed treason, a crime punishable by death. When Othello looks within, he sees a man who is inferior to Cassio, and he is convinced that Desdemona is lost, and that she must be executed. Even then, he feels the need to question her (although that does no good since he has already judged her) and to spy on Cassio, who he believes confesses to an affair with his wife. In a military state such as Cyprus, Othello, as the acting head, has the authority to execute these transgressors--in the name of justice. He is wrong; he is not stupid.
Othello is very intelligent. First, he is light years ahead of his time in terms of what a black man, a former slave, and a former Muslim could accomplish in a white-dominated, Christian Euro-centric world.
He is appointed General of the Venetian forces and sent to Cyprus, front lines against the Turks. He wins appointment ahead of other qualified officers, namely Iago (who I deem to be extremely intelligent). And Othello wins against the Turks, with the help of a storm. He survives nonetheless and is credited a victory at sea.
Othello is a brilliant public speaker. He defeats not only Brabantio in court in Act I, but his speech is so moving (full of pathos) that the Duke says he too might well give his daughter to marry Othello, under the circumstances.
So, he is a military mastermind and a great orator in court. This is the case with many men: good at aggression; good at public speaking; bad at matters of the heart; bad in private. Othello is what Deborah Tannen might call good at "Report-talk," bad at "Rapport-talk."
I wouldn't all him stupid, but he is so full of male pride regarding his reputation that he falls vulnerable to Iago's tricks. He closes down intimate communication with Desdemona. This, of course, leads to problems in relationships: anger, violence, divorce, and--in this case--murder (an honor killing). In short, Othello He falls prey to the sexist beliefs of his era, causing him to reify Desdemona; he turns her into a trophy wife and status symbol, which he destroys in order to protect his reputation.
The idea that Othello is too stupid to be called a tragic hero needs to go a bit deeper. In the play Othello by William Shakespeare, the tragic hero is shown at first as confident, skilled - a man at the top of his game despite all the discrimination and hurdles he has had to overcome. So stupidity is clearly not a word that is precise enough. I prefer the word gullible and emotional and psychologically vulnerable. For example, underneath all the bravado of a man who is lauded for his wits and courage in battle probably lies a history of slights and humiliations regarding color or age. I think Othello actually presents as a man with low self-esteem, insecurity and buttons that are all too easy to press. Iago finds them.
I guess I would disagree with this read of Othello as a character. Certainly, his intelligence would have to be on a very high level in order to be a strong military leader, one to be entrusted with a governorship. His curse is his demons of doubt and insecurity that are tapped by Iago. This does not make him stupid, but rather makes him ultimately human. He is an very honorable and intelligent figure who is victim to his own ghosts of self doubt in terms of his relationship with Desdemona. I don't see this as stupidity. It is a highly human trait to doubt a beloved. The fact that Othello capitulates this his human elements does not prove stupidity, as much as it proves humanity.