In Othello, why does Iago carefully observe the way Cassio greets Desdemona?
The answer to this question can be found in Act II scene 1, which is when Iago observes very closely the kind of body language that Cassio displays when he greets and talks with Desdemona. In an aside, he reveals to us why it is precisely that he is paying such close attention to such activity, and what he plans to do on the basis of it:
He takes her by the palm: ay, well said,
whisper: with as little a web as this will I
ensnare as great a fly as Cassio. Ay, smile upon
her, do; I will gyve thee in thine own courtship.
You say true; 'tis so, indeed: if such tricks as
these strip you out of your lieutenantry, it had
been better you had not kissed your three fingers so
oft, which now again you are most apt to play the
sir in. Very good; well kissed! an excellent
courtesy! 'tis so, indeed. Yet again your fingers
to your lips? would they were clyster-pipes for your sake!
He is clearly going to use the very warm way in which Cassio converses with Desdemona to plant a seed of jealousy in the mind of Othello. By doing this, he hopes to get his own back on Cassio for being promoted instead of him and also to get his revenge on Othello by trying to insinuate that his beloved wife is actually cuckolding him with Cassio. The image that he uses of "ensnaring" suggests that he sees himself as a kind of spider that is trying to capture and tie up other characters, like Cassio, who is the "fly" in this example.