These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
A possible motive for Iago is class-resentment, and indeed, this is the only motive he expresses with any consistency.
Racist interpretations of the play sometimes see Desdemona as am empty-head strumpet who only marries Othello because she can't control her libido and condemn her for "miscegenation". See the quotation from John Quincy Adams below.
Of course, Adams' frothing about Desdemona's 'betrayal' of duty, race, sex and country also stems from his ideas about everything women should be striving for- to be the perfect consorts of men like their own families (and betraying ones own sex presumably meaning not keeping women of ones own station an exclusive commodity to men of your own status or preferably higher, therefore presumably degrading their value), and churning out sons in the image of your own people. Desdemona's relationship with Othello is in this respect behaving as if she's her own individual person, rather than a conduit for Venetian sons- unforgivable.
There are alternative views of Othello himself: Hero, fool or downright monster? The critic John Sutherland noted that in the original story, Shakespeare's source material, the unsympathetic Othello-equivalent plotted with the Iago-equivalent about how to kill his wife in a way that wouldn't leave a mark/would look like natural causes, so that he could escape punishment and could maintain his position. While Shakespeare's Othello is way more sympathetic overall, there's a few lines that indicate that he too attempted such a plan, putting him in a worse light. Sutherland also discusses how despite making grandiose claims about his handkerchief, in other instances, Othello treats it like a normal handkerchief, and his later obsession with it has elements of Believing Their Own Lies.
Draco in Leather Pants: Modern productions tend to be more sympathetic towards Iago, perhaps overly so. The fact that he was once played by Kenneth Branagh—and more recently by Ewan McGregor—doesn't help.
Ensemble Darkhorse: Emilia, Iago's wife and Desdemona's maid, has been extremely popular throughout much of the play's history for the way she excoriates unfaithful husbands in a touching monologue in the fourth act, chews out Othello for his crime, and delivers the fatal blow to her own husband's Evil Plan, gets stabbed, and then keeps going. In fact, it was not uncommon at certain points for her to be billed above her mistress, the play's ostensible heroine.
Fair for Its Day: In the original story on which Othello is based, the Moorish character doesn't even have a name, and it ends with Desdemona lecturing the audience on why interracial marriage is evil. In his adaptation, Shakespeare gives the Moor a name and fully fleshes out his character into a sympathetic war hero. Shakespeare also adds the character of Iago to serve as the play's villain, a white man who manipulates Othello into a jealous rage For the Evulz. In fact, the only overtly racist elements of the play are spoken by unsympathetic characters.
Ho Yay: Some scholars — and many a high school English teacher — have proposed that Iago's true motivation is unrequited love for Othello. You can find evidence for this in his dialogue.
Then again, you can find evidence for at least a dozen, often conflicting, motivations in his dialog. He also says he has no reason at all. See also For the Evulz.
Might be a case of a deliberate Multiple Choice Past, to emphasize that Iago is an unrepentant liar..
For some Iago's description of Cassio in bed with him and "sleep humping" might fit this.
An oft-cited piece of evidence for this possible motivation is the scene wherein Iago and Othello initiate a pseudo-wedding ceremony. To each other.
Othello:*kneels* In the due reverence of a sacred vow
I here engage my words.
Iago: Do not rise yet. *kneels*
Witness, you ever-burning lights above,
You elements that clip us round about,
Witness that here Iago doth give up
The execution of his wit, hands, heart,
To wrong'd Othello's service! Let him command,
And to obey shall be in me remorse,
What bloody business ever.
Othello: I greet thy love,
Not with vain thanks, but with acceptance bounteous,
Mary Sue: Desdemona, depending on character interpretation. She's as pure as the driven snow, and every bad thing that happens to her is someone else's fault. She's a total martyr. Of course, that's the whole point.
She could qualify as a deconstruction as well, given how all her Sueness does is serve to screw her over. After all, would Iago have wanted to bring her down if she was any less as such?
Nightmare Fuel: There is something deeply unsettling about the character Iago. The idea that someone you trust implicitly could be so sociopathic that the first minor, unintentional sleight you perpetrate against them could lead them to utterly destroy your life for kicks is very creepy.
Stabbing his own wife without the slightest hint of regret or reluctance.
The Scrappy: Starting in the eighteenth century, Desdemona's character was heavily bowdlerised to remove the more subversive elements and make her nothing other than a demure, passive, innocent victim with all the personality of a damp piece of paper. This characterisation stuck for most of the next 300 years, and made her exceedingly unpopular amongst both actors and the audience. The actor William Macready warned Fanny Kemble thusly before she took on the role (and actually turned out to be one of the more successful and spirited Desdemonas of the time):
"... there is absolutely nothing to be done with (the part of Desdemona), nothing; nobody can produce an effect in it; and really, Emilia's last scene can be made a great deal more of. I could understand your playing that, but not Desdemona."
Rescued from the Scrappy Heap: As feminism began to seriously kick off in the twentieth century, new attention was paid to the traditionally-disdained character of Desdemona. The especial turning point is usually seen as Maggie Smith's tough, angry Silk Hiding Steel performance in 1964, which encouraged later productions to put much more fight and sexuality in their Desdemonas after a long period of passive, chaste bowdlerisation. Even the more demure versions since then have become more prominent and central more often, with their tragedy being emphasised rather than being sidelined to better serve the interplay of Othello and Iago.
Values Dissonance: Now you have to understand - Elizabethan-era morality was different from modern morality. Iago says in the play "I am not what I am," and to a modern reader this means "I'm not what I act like." To an Elizabethan, it means something completely different: Iago is the absence of existence, which makes him the ultimate villain: evil in Elizabethan days wasn't considered to be a thing, it was considered to be the absence of God. Iago is the absence of God, making him even more evil than other Shakespearean villains.
It's also worth mentioning that some readers won't understand that when Othello gives up Christianity, he super-damns himself to Hell; that's even worse than just being a pagan.
This phrase has been taken by some scholars as a subversion of St John's "By the grace of God, I am what I am".
Or God's "I am who am" answer to Moses in Exodus 3:14.
More obviously: these days, a black man marrying a white woman would not raise many eyebrows. Back then, not so much.
Vindicated by History: Even more than usual for Shakespeare - he subverted a lot of Forgotten Tropes at a time when a Cliché Storm was expected. Thomas Rymer's Short View of Tragedy in 1693 summed up the response to, for instance, a soldier as a villain rather than an honest man, and a dropped handkerchief leading to multiple murders rather than a comical misunderstanding.