In Othello, the major symbols that represent the dualities of loyalty and betrayal are the rank of Lieutenant, the handkerchief, and, quite simply, words.
Iago is insanely jealous that he was passed over for this rank. How could Othello give the rank to a younger, less experienced bureaucrat like Cassio? As a result, Iago hates the Moor and vows revenge. In his plan, Iago gets Cassio drunk and into a fight so that Othello strips Cassio of the rank, leaving it an open position for Iago to fill. So, by the end, the disloyal Iago aligns himself with Othello, and they plot to murder both the loyal Desdemona and loyal Cassio. Dramatic irony at its finest.
"There's magic in the web of it." The handkerchief is a symbol of morbid love and jealousy to Othello. Whoever is in possession of it is also in possession of Othello's extreme emotions. It is a magical kind of puppet-master that controls loyalty and betrayal throughout the play. Everyone has his hands on it: Othello, then Desdemona, Emilia, Iago, Cassio, and Bianca. It goes from a loyal lady to a prostitute, and when Othello sees it in possession of a woman other than Desdemona, he vows to kill his wife for infidelity.
He who controls language controls others. Like the devil in the Garden of Eden, Iago uses words to tempt his subjects. His words publicly seem to be honest, but privately we and Roderigo know they are lies. Othello calls Iago "honest" throughout the play, a word synonymous with loyalty. By baiting Othello toward jealousy and murder, Iago successfully takes away language from the Moor and causes him to become a mute beast. This "Beauty and the Beast" is no fairy tale that ends happily ever after.