Shakespeare begins the play with two secret acts. What is the deception and the effect that these deceptions have on the tone of the play?

One of the secret acts is the marriage between Othello and Desdemona. The two marry in such a way because Desdemona's father, a senator, would never want her to marry a foreigner and a black man like Othello, even though Othello is an important figure in Venice.
While Desdemona's deception of her father is not meant to be malicious, it does have consequences which reverberate throughout the play. Desdemona's father warns Othello that Desdemona's willingness to deceive her own father means she'll have no qualms deceiving a husband, and Othello comes to deeply suspect Desdemona of infidelity even on the slimmest and most trivial evidence, in large part because of this deception.
Another secret act in the opening of the play is how Iago and Brabantio get Desdemona's father out of bed. They cry out, "Thieves!" This is a small deception, but it does set up something important about Iago—he is never what he seems and is willing to use lies to get people to act as he desires.

The play opens with Iago and Roderigo conspiratorially discussing the Moor, in darkness; the tone of the opening scene, in which Iago declares that "in following the Moor, I follow but myself," sets the tone for a play characterized by Iago's duplicity and self-interest and deeds conducted in shadows and secrecy. Ostensibly, Iago is annoyed that Cassio has been made Othello's lieutenant, and Iago only his "ancient" ("I had rather been his hangman," says Cassio). He feels that he was deceived in this matter, and therefore declares "I am not what I am"—a note to the audience that his motives will never be transparent—and sets himself to lowering Othello in social position, as he feels him to be "puffed up."
Next, Roderigo and Iago call out Brabantio under false pretenses—"Thieves, thieves!"—so that they can tell him that his daughter, Desdemona, is currently "making the beast with two backs" with Othello. This second part does turn out to be true, but the audience knows that Iago is calling Brabantio's attention to it not truly out of concern for Brabantio but out of a desire to lower Othello in the estimation of the nobleman.
The contrast between the first and second scene sets the tone for Iago's duplicitous behavior throughout the play, as we here see him declaring his devotion to Othello and fury at Brabantio for having accosted him—although we of course know that it was Iago who sent Brabantio to do this. Iago, we see from the beginning, cannot be trusted. Indeed, perhaps his comment that he does everything in his own self-interest is his only true statement in the play.