I think that Othello should bear some of the responsibility for his predicament. As a soldier, I don't think he would have it any other way. Yet, having said this, it might not be entirely accurate to place the entirety of blame at his feet. Iago is the agent of action and must be seen as the cause of human suffering in the drama. To avoid assigning blame to Iago almost fulfills more of what he would have wanted. In the end, we can see that Othello made terrible mistakes that were not intentionally cruel. They amounted to unintentional cruelty, and thus he is responsible in this regard. However, when looking at someone who is deliberately cruel and thereby must assume a greater level of responsibility for what happens, Iago becomes the agent of action.
Othello is to blame for his downfall because of his insecurity. Othello's inability to control his own sense of doubt and uncertainty are the elements that cause his downfall. This condition results in because of both external and subjective elements. From his own point of view, Othello never quite overcomes the fact that Desdemona picked him. Undeniably, he is in love with her. However, it becomes clear that he never fully accepts the fact that he was worthy of her choice. In this regard, he becomes easily susceptible to Iago's manipulations. Othello's love for her is more than simply affection. It reveals an almost surprised element to have been chosen, as seen in Act II, sc. 1:
It gives me wonder great as my contentTo see you here before me. Oh, my soul’s joy!If after every tempest come such calms,May the winds blow till they have wakened death,And let the laboring bark climb hills of seasOlympus-high, and duck again as lowAs hell’s from heaven! If it were now to die,'Twere now to be most happy, for I fearMy soul hath her content so absoluteThat not another comfort like to thisSucceeds in unknown fate.
Then must you speak/Of one that loved not wisely, but too well./Of one not easily jealous, but being wrought,/ Perplexed in the extreme. Of one whose hand, /Like the base Indian, threw a pearl away /Richer than all his tribe. Of one whose subdued eyes, /Albeit unused to the melting mood, /Drop tears as fast as the Arabian trees /Their medicinal gum. (Act V, sc. 2)