How can it be proven that Othello is too trusting, especially of Iago?
I think that one way it can be proven that Othello is too trusting lies in his willingness to embrace reductive notions of the good. This aspect of his "tragedy in character" exists in Othello's lack of a calibrated construction of trust. The insecurities that plague and gnaw at him result because his nature is inclined to trust too much, arising from a flawed view of how human beings are supposed to behave.
Othello believes in people far too much. This enables him to be placed in positions where manipulation is easy. He trusts Iago, believes too much in Cassio, and worships the idea of Desdemona. In many regards, Othello is a soldier, one who follows blindly and believes in the structure that governs human action. Othello believes the "chain of command" that guides individual behavior is a good one, and does not think twice about how people might not be as they appear.
Naturally, Othello's fatal flaw is in his trust of Iago. However, the character flaw of being too entrusting can be seen in his idealizing Desdemona. When Othello says, "she had eyes and chose me" (III.iii.189), it is clear that he trusts her so much that he could not consider anything less than a perfect vision of her in his own mind. He is able to develop this vision of Desdemona because of his trusting nature, one that vaults her to an almost inconceivably elevated condition in his own mind. Like a solider, Othello's entrusting nature sees people as either allies or enemies, friend or foe. He is so trusting that he fails to see the complexities that exist within human beings. Othello's trusting nature can be seen in his final words when he claims to be one "that lov'd not wisely but too well." This helps to solidify his trusting nature, one that dooms him to pain.