It’s hard to pin down exactly what the speaker is like in Shakespeare’s poem—and that’s exactly the point. The reason for this is the speaker is incredibly conflicted, torn this way and that by different emotions. To begin with, you’ve got the over-arching movement of the poem, which begins in quatrain 1 by blaming "Love" for the speaker’s misery, and continues blaming him in quatrain 2.
Then, in quatrain 3, the speaker changes course and blames his own heart and eyes for continuing to make him think that his lady-love is loyal. In the couplet, those concluding two lines of the poem, the speaker continues to blame the heart and eyes of the speaker. Thus, in one sense, you can see the speaker changing his mind as the poem rolls along. He starts by blaming somebody else (a god, as it so happens), but then kind of says to himself, "Okay, okay, I know, it’s my own heart and eyes who are to blame." But even this is a little weird, right?
The speaker blames his heart and eyes like they’re not part of him. It’s like they’re separate beings or something. So, even though it looks like he’s accepting responsibility for being deceived, he is still sort of diverting blame from himself by the end of the poem.
But isn’t this discussion of blame leaving somebody out? Yes: the speaker’s mistress, the lady all the fuss is about. Here, too, we see a mix of emotions. On the one hand, he describes her in terms that suggest vehement dislike, or even disgust (how else do you interpret calling someone a "plague"?).
On the other hand, it’s worth noting that the speaker diverts most of the blame onto Love and parts of his own body—as if he thinks the lady can’t be entirely blamed for her own nature of being a cheater. This might be a sign of what the speaker has been telling us all along—that he’s still totally head-over-heels for this girl, even though he knows she’s bad for him. So, here you have another layer of complexity and self-contradiction in the speaker’s character.
That said, there is one big factor that remains a constant in the speaker’s personality from the beginning of the poem to the end: his love of words and wordplay. From the double meanings of "see" in line 2, to those crazy obscene metaphors in quatrains 2 and 3, to the many (obscene) meanings of "false plague" in line 14, you can tell that this guy has a serious love of language. Do you have the same impression we do, that the wordplay gets most intense in this poem when the speaker is feeling the most intense emotions? If so, you could almost say that wordplay, for the speaker, is a coping mechanism, a way of getting out all the seething anger, lust, and jealousy that comes out in his relationship with this mysterious lady.