What is the effect of Iago's honest reputation on the other characters in Othello?
You are right to focus on the way that other characters view Iago in this Shakespearian tragedy. It is clearly this position of being considered an "honest" man that gives Iago the opportunity he is looking for to manipulate and betray others. In particular, he is able to bring about various plots against his superior, Othello, who, as it is shown in Act I scene 3, trusts him completely. Note how he describes Iago to the Duke in this scene:
So please your grace, my ancient:
A man he is of honesty and trust.
He then addresses Iago by calling him "Honest Iago." Clearly, it is the mistaken confidence that Othello places in Iago that gives Iago free rein to devise his various plots and stratagems and gain the revenge that he so desperately wants against the perceived slight that embitters him so greviously. The way in which he abuses the trust of other characters and manipulates them would not have been possible were he not to have had such a high reputation to begin with.