One of the gaps would be Othello and Desdemona's wedding. We know that they went off and eloped, but we don't know the details of the wedding. Also, we know little about their brief courtship, except what Othello tells the senators during his speech to them. There are also gaps/silences about how Othello came to be such a powerful general (we know that he is strong and smart, but this is general information). We don't really know how he rose through the ranks, for example.
Gaps in Othello relate to time shifts, and background information.
With relation to time, the play does not examine the travel of characters from Venice to Cyprus. In addition, Shakespeare uses a 'double time mechanism'. This means that the actions in the play is disproportionate to facts of the plot. For example, Othello believes that desdemona infidelity has been going on for weeks, however the time span of the play is little over 3 days.
With regards to information, the play does not provide information in relation to the background of Othello or iago. In addition the action involved in the courtship is unknown to us.
Also Iago is a mystery to the audience. How did he come to hate Othello so much? What was his life like? We know nothing of his childhood and how he developed into the man he was. If we knew this, it could give us insight to the reasoning of his actions.