I was of three minds, Like a tree In which there are three blackbirds. (Section II)
The expression "to be of two minds" is a commonly used idiom that means "to be undecided between two opinions or desires."
I do not know which to prefer, The beauty of inflections Or the beauty of innuendoes, The blackbird whistling Or just after. (Section V)
We don't think the speaker means to suggest he's actually torn between these two things. The problem doesn't keep him up at night. What he means is something along the lines of, "The whistling of the blackbird is really beautiful, even when it's not whistling."
O thin men of Haddam, Why do you imagine golden birds? Do you not see how the blackbird Walks around the feet Of the women about you? (Section VII)
The men of Haddam choose to ignore the blackbird in favor of a mythical "golden" bird that they'll never be able to find, unless they know something that the rest of the world doesn't. The poem implies that they ignore the lovely feet of the women around town, because if they were looking at the feet, surely they would have noticed the blackbird.
In that he mistook The shadow of his equipage For blackbirds. (Section XI)
Aside from sharing the same black color, we find it hard to believe that anyone would mistake a shadow for a bunch of blackbirds. But it's OK: we're used to unexplainable mystery in this poem by now.