1.  We must not suppose that Othello’s account of his courtship in his famous speech before the Senate is intended to be exhaustive.  He is accused of having used drugs or charms in order to win Desdemona; and therefore his purpose in his defence is merely to show that his witchcraft was the story of his life.  It is no part of his business to trouble the Senators with the details of his courtship, and he so condenses his narrative of it that it almost appears as though there was no courtship at all, and as though Desdemona never imagined that he was in love with her until she had practically confessed her love for him.  Hence she has been praised by some for her courage, and blamed by others for her forwardness.

But at III. iii. 70 f. matters are presented in quite a new light.  There we find the following words of hers: 

                             What!  Michael Cassio,
     That came a-wooing with you, and so many a time,
     When I have spoke of you dispraisingly,
     Hath ta’en your part.

It seems, then, she understood why Othello came so often to her father’s house, and was perfectly secure of his love before she gave him that very broad ‘hint to speak.’  I may add that those who find fault with her forget that it was necessary for her to take the first open step.  She was the daughter of a Venetian grandee, and Othello was a black soldier of fortune.

2.  We learn from the lines just quoted that Cassio used to accompany Othello in his visits to the house; and from III. iii. 93 f. we learn that he knew of Othello’s love from first to last and ‘went between’ the lovers ‘very oft.’  Yet in Act I. it appears that, while Iago on the night of the marriage knows about it and knows where to find Othello (I. i. 158 f.), Cassio, even if he knows where to find Othello (which is doubtful:  see I. ii. 44), seems to know nothing about the marriage.  See I. ii. 49: 

Cas. Ancient, what makes he here?

Iago. ’Faith, he to-night hath boarded a land carack: 
If it prove lawful prize, he’s made for ever.

Cas. I do not understand.

Iago. He’s married.

Cas. To who?

It is possible that Cassio does know, and only pretends ignorance because he has not been informed by Othello that Iago also knows.  And this idea is consistent with Iago’s apparent ignorance of Cassio’s part in the courtship (III. iii. 93).  And of course, if this were so, a word from Shakespeare to the actor who played Cassio would enable him to make all clear to the audience.  The alternative, and perhaps more probable, explanation would be that, in writing Act I., Shakespeare had not yet thought of making Cassio Othello’s confidant, and that, after writing Act III., he neglected to alter the passage in Act I. In that case the further information which Act III. gives regarding Othello’s courtship would probably also be an after-thought.