I would argue that Othello is largely episodic, because it is expansive and structurally somewhat diffuse. One might think that the fact the play opens in Venice, and then the action moves to Cyprus, is an arbitrary choice on the part of Shakespeare. Iago's verbosity and the expansiveness of his plotting against Othello, plus the presence of characters who have little direct bearing on the story, are episodic features as well.

Try to think of Othello in comparison with a play like Macbeth. The latter is much more concise, and the action in it moves more quickly, than in Othello. In Othello, Shakespeare spins out scenes with repetitions, such as Othello's demands to Desdemona to give him the fateful handkerchief. Also, you might wish to familiarize yourself a bit with the operatic adaptation by Giuseppe Verdi of Othello. Verdi's librettist Arrigo Boito excised much of the material in the play and tightened the structure, creating a drama which some people (opera buffs of course!) have even considered dramatically superior to Shakespeare's original.

Shakespeare's manner is sometimes to give an expansive, almost wordy quality to his characters' speeches. Things that could be said briefly are often extended for poetic effect. I say this not, of course, as a criticism. You might ask yourself whether this is a characteristic of Shakespeare that differentiates him from other dramatists of his period, if you get a chance to read Marlowe's work, for instance. Or, though it's obvious that, as I've indicated, Macbeth is a more compressed drama than Othello, is Othello more typical of Shakespeare's general approach, or is it unusual in the degree to which its structure is episodic?

A climactic plot structure will normally begin late in the story, very close to the climax of the play. It will normally cover a very short space of time, roughly a few hours or at most a few days. It occurs in a very restricted location such as one room and involves very few characters, up to a maximum of about 6 to 8. The plot is linear and moves forward without any form of interruption and there is no sub-plot.

By contrast, an episodic plot begins very early on in the story and moves through a series of episodes over a much longer period of time. It has several characters and several different locations. The plot of such plays is also marked by two or more different strands such as a sub-plot and a central plot.

Bearing these differences in mind, we can see that this play is clearly episodic in terms of its plot structure. The play has a long time span, moves between a number of different locations and begins towards the beginning of the action rather than just before the climax when Othello kills his wife. Such an episodic plot enables us to see Iago's scheme being hatched and how he works on so many different characters slowly but surely. Remember what Iago says about himself in Act I scene 1:

Heaven is my judge, not I for love and duty

But seeming so, for my peculiar end,

For when my outward action doth demonstate

The native act and figure of my heart

In complement extern, 'tis not long after

But I will wear my heart upon my sleeve

For daws to peck at: I am not what I am.

Having declared this about himself at the beginning of the play, an episodic plot structure allows Shakespeare to develop the character of Iago through seeing how he relates to various different individuals and how he hatches his plot to gain his revenge against Othello and various other characters.