While Othello gets lumped in with the tragedies, that’s really only because the protagonist kills himself after killing his wife. Sure, it makes the audience cry, but you could do that just as easily by killing puppies or kittens. And isn’t that the very basis of melodrama, appeal to the emotions via machinations of plot?
There’s really no dramatic tension beyond “what will happen next?” It’s not like Iago is ever in danger of getting caught, or things go wrong for him. He’s master of the events just as surely as the Duke is in Measure for Measure. As far as characterizations go, Desdemona is the quintessential virtuous maid, Othello is the football player type, a good guy, but more brawn than brain, Roderigo the gullible fool, Cassio the basically nice guy who makes one fatal mistake. The only character with an ounce of humanity is Emilia, who conveniently for the plot, manages to overlook Iago’s true nature until the end of the play.
Now I’ll admit that Iago isn’t a cardboard villain, the evil banker forclosing on a mortgage or what have you. He’s clearly got mental health problems. He’s paranoid (he believes that at least two other people are sleeping with his wife despite having no evidence), and he’s a megalomaniac. Despite being basically a general’s errand boy, he think he ought to be running the place, to be the general himself. And I’m not denying that people like that exist, look at the Unibomber as a case in point. The main problem is that Iago controls the plot.
As for racism, I would say that’s pretty apparent. I’m not saying Shakespeare himself was a racist, at least no more than was typical for his era. After all, Queen Elizabeth twice ordered the deportation of “great numbers of Negars and Blackamoors which … are crept into this realm.” Brabantio, Desdemona’s father, is clearly racist. He doesn’t believe a white girl could fall for a black man unless voodoo was involved.
It’s not clear whether Iago is or not, he’s certainly willing to use the racism of others to get what he wants, and in the very first scene he’s there with the animalistic metaphor “an old black ram is tupping your white ewe.”
More disturbing is when Othello himself disparages his blackness, and finally that the couple that dared marry across racial bounds are killed. A bit of a warning against those “unnatural” liaisons, don’t you think? After all, Othello not only says “for I am black and have not those soft parts of conversation that chamberers have”, but he buys into Iago’s argument that if Desdemona is willing to do something so unnatural as fall in love with a black man, she’s liable to do anything.
For all the (justifiable) complaints about how The Taming of the Shrew is misogynistic, I’m surprised that the racism in Othello doesn’t get called out to the same degree. Arguing about how noble Othello’s actions are when he realizes his error doesn’t hold much water for me if you’re also sending the message that the only good blackamoor is a dead one.