Many people have questioned Iago's sexuality. More than any other character's, his comments are charged with homeoerotic suggestiveness. He has little affection for women (even for Emelia, his wife) and what affection he is capable of seems to be directed more towards men. He says things like, "I think you know I love you" when speaking to men. Is he "in love" with Othello? Hard to say. All he ever admits to is hatred (a strong emotion that sometimes follows thwarted love), but he says his hatred is because of the rumour that Othello has slept with Emelia.

It is possible that he hates Othello for loving Cassio more than him. He certainly speaks of that when he complains about Cassio's promotion, and there's also that troublesome reference to the "daily beauty" Cassio has in his life that makes Iago "ugly" in comparison.

As for how Iago's possible homosexuality affects the play, it's hard to say. Sometimes men had relations with men while retaining their relationships with women. Iago, being married, might have been such a man. Was Othello? Did Othello ever reciprocate the love? Did he transfer his affections to Cassio? (Cassio is careful not to let Othello see that he is "womaned"--although the standard reading of this is that it would make him look a less fit soldier). The play isn't often considered a love triangle, but...