Sure, "The Dance" doesn't have any kind of regular rhyme scheme, but that doesn't mean that Williams doesn't make great use of sounds in this poem. Did you happen to catch how many B words there are in this short little poem? We're not just talking about "Brueghel" here, either. Here's a hint: tons. "Blare," "bagpipes," "bugle," "bellies," "balance," "butts"—the list goes on. The effect of all this alliteration is a continuous bouncing feeling that helps you bound through the lines along with the dancers.
Williams also plays around with rhyme throughout. Mostly, he goes crazy with words that rhyme with "round." Early in the poem he tips us off that this sound might just reoccur by repeating it several times: "the dancers go round, they go round and/ around" (2-3).
Not long after he reuses "round" again, but this time plays on a different meaning of the word by saying that the "bellies" of the dancers are as "(round as the thick-/ sided glasses whose wash they impound)" (5-6). We're guessing you also noticed that he rhymed "round" with "impound" there as well. Later in the poem, WCW hits us up again by describing the "Fair Grounds" where the kermess is taking place, and saying that the dancers' "shanks must be sound."
So, yeah, there's no doubt that Williams had a lot of fun coming up with things that either rhymed or near-rhymed with "round." But what do you think might be the point of that? Is it just random poetic thing to do, or is it somehow tied into the meaning of the piece? To us at least, the repetition of this sound adds to the circular, swirling motion of the poem. We talk about how the poet achieves this rhythmically in "Form and Meter," but it seems that he achieves this sonically as well.
The fact that this rhyme comes back again and again—particular as an internal rhyme and not an end rhyme—gives us a sense of the whirling of the dancers and is aided by the fact that it's all rhyming with the word "round." That this is an internal rhyme adds to the inner-twisting motion of the poem as a whole. It's constantly turning in on itself to echo. We think it's also really effective that the rhymes don't come back into any kind of rigid scheme. Yeah, they create a sense of circular motion, but not all circles are perfect, especially not ones created at raucous festivals like the one seen in "The Kermess."