The only moving thing Was the eye of the blackbird. (Section I)
At several places in the poem, the speaker juxtaposes (places side by side) images of vast landscapes and the blackbird. He makes the blackbird seem totally powerful and mysterious by making its eyeball the focal point of the whole scene. To the imagination, that eye seems as big as the giant eye of the T-Rex in that famous scene from Jurassic Park.
I do not know which to prefer, The beauty of inflections Or the beauty of innuendoes, The blackbird whistling Or just after. (Section V)
The use of complex vocab-words like "inflections" and "innuendos" actually makes the speaker sound less amazed. He puts his intense feelings into intellectual terms.
The mood Traced in the shadow An indecipherable cause. (Section VI)
One of the reasons the blackbird is so amazing is that it inspires the speaker's imagination. The sensations caused by the sight of the blackbird are indescribable, so he's left with vague, hard-to-follow expressions like "mood traced in the shadow" and "indecipherable cause."
When the blackbird flew out of sight, It marked the edge Of one of many circles. (Section IX)
Again, the speaker's imagination creates the reality surrounding the blackbird. He's not just amazed by the bird; he's amazed by the circles.
Even the bawds of euphony Would cry out sharply. (Section X)
It's hard to rouse those "bawds of euphony," who usually only get excited by very harmonious sounds and images, but the blackbird has them crying out in amazement.