Othello and the others learn the truth when Emilia tells them about the handkerchief:
"Oh, thou dull Moor! That handkerchief thou speak'st of
I found by fortune and did give my husband;
For often, with a solemn earnestness,
More than indeed belonged to such a trifle,
He [Iago] begged of me to steal't." (V, ii)
According to David Bevington's The Necessary Shakespeare (2nd ed.), Othello looks at Iago's feet to see if he had cloven feet like the devil. Now, that doesn't mean he really thought Iago might have cloven hooves - it's Shakespeare being metaphorical and demonstrating that Othello has finally learned that he's been led astray the entire time by Iago.