In both plays there is alot of dramatic irony but also shows revenge and jealousy...
The most obvious subject or theme in Othello is revenge and jealousy. Iago is the main kead to almost everything that happens in these themes. He has been hearing rumours about his wife's affairs with the moor, so he dislikes Othello and must be jealous of Cassio for being lieutenant. However, we can never be completely sure what Iago's motivation is to be so destructive - he manages to get Cassio dismissed but then Iago doesn't seem interested in Cassio's job, only in causing more problems. We also learn that Iago has tried many times in the past to steal the handkerchief that means so much to Othello.
This tells us that he was planning against Othello long before his promotion was blocked.
Jealousy affects most other characters as well. Othello cannot bear the fact that his wife might be having an affair and Iago cleverly plays on this. For instance, when Othello thinks his wife is honest and needs proof of the affair, Iago asks if he would want to see her 'topped' (i.e. with a man on top of her) but then tells Othello to calm down and that his mind 'perhaps may change'. Of course it won't - Iago presents the worst image possible to Othello knowing the damage it will cause.
Jealousy affects almost all of us at sometime in our lives, and Shakespeare shows the destructive effects it has throughout the play. In fact only two characters seem unaffected by jealousy - Desdemona and Cassio. Desdemona dies, but everyone realises what a good woman she was, and Cassio is rewarded by taking Othello's place as general (and by deciding Iago's punishment).