I think that one point that has to be made on Othello's jealousy is in its uncontrollable nature.  Once Iago plants his "medicine" in Othello's mind, it grows and cannot be stopped.  Like weeds in a garden, this jealousy dominates Othello.  He cannot control it and it cannot be stopped. It spreads everywhere and contaminates everything.  Jealousy is shown as a limitless monster, rooted in the individual.  It is shown to be impossible to control.

Another point to be made on Othello's jealousy is that it prevents any open and full discussion.  I tend to think that the entire tragedy could be resolved if Othello is able to sit and reasonably talk about his fears and insecurities with Desdemona and Cassio.  If he is able to simply talk openly about his fears and his insecurities, he could receive validation that would help him.  His jealousy is shown to take such a control over him that he cannot speak openly about it, allowing it to fester even more.

Finally, I think that Othello's jealousy is rooted in a personal sense of insufficiency and insecurity.  Othello suffers from an insecurity that is personal in nature.  To a great extent, he does not believe himself as being worthy of such great endeavors and a wife like Desdemona.  He might believe this because he has internalized how society feels about a man of color and an outsider like himself.  This sense of insecurity and doubt enables his jealousy to take hold over him.  It is this lack of self worth that allows jealousy to assume such a control over his life and drive his downfall.

What are the arguments about the jealousness of the characters in Othello?

Jealousy runs throughout Othello. Jealousy is both resenting someone else for their achievements, often because you feel you deserve what they have gotten, and wanting to guard what you have from others.

Iago's jealousy of Cassio for being promoted over him sets the plot in motion: Iago's anger at his talents being, in his opinion, underrated leaves him fuming with suppressed rage and determined to destroy both Cassio and Othello.

Iago's twisted jealousy expresses itself in a desire to destroy Othello's happiness with with his bride Desdemona, as well as Othello's trust in Cassio. On hearing of the marriage, Iago first tries to incite Brabantio, Desdemona's father, into thinking of it as a virtual abduction and rape by a black man of a white woman. This does not work, as Desdemona is able to convince her father that she is in love with Othello and married him freely. This leads Iago to try a new tact: insinuating to Othello, who is insecure about his age and race, that Cassio and Desdemona are having an affair right under his nose. He also gets Cassio drunk so that Othello dismisses him from his post.

Insecure, and wanting his wife to himself—being jealous of her attentions paid to any other man—Othello accepts Iago's framing of what is an innocent friendship between Cassio and Desdemona as a sordid, ugly affair. He is so jealous of this imagined affair that he ends up killing Desdemona rather than having her, as he thinks, be sexually involved with another man.

In Othello, Shakespeare shows that jealousy is a poisonous trait, a form of madness that leads people to evil acts.