Yes, it looks mighty concise with only three sections divided into four couplets for each stanza. And since most of the couplets are in perfect rhyme, we might feel compelled to dig deeper for a particular meter. After all, classical poetry was all about form and meter. Since "Ars Poetica" is a sort of homage to Horace's take on classical poetry, maybe we'd expect some dactylic hexameter or some other funky, complex metrical form.
But the assumptions stop there. In fact, we notice a few lines that may look like couplets but don't have any sort of rhyme, like lines 21-22. So MacLeish has managed to create a poem that is a kind of paradox of itself, appearing to go one way, but then juking out the reader and veering off in another direction. And since MacLeish was a modern poet, we had to expect that the guy was digging the whole free verse trend. After all, if he had written the poem with a particular form and meter in mind, how can we really take the words, "a poem should not mean but be," very seriously?
"Ars Poetica" tends to "be," really, whatever it wants to be. One minute we have perfect couplets like, "dumb" and "thumb" (3-4) and the next we have slant rhymes like "releases" and "trees" (11-12). Those slightly more imperfect rhymes remind us that this is indeed a modern poem that's not looking to drum a bunch of sing-song rhymes into our heads. Still, the more perfect rhymes appear as a sort of nod to MacLeish's predecessors who were kind of sticklers for rhyme and meter.
Then by the very end, our speaker throws in another kind of alternating rhyme between lines 21-24, rhyming "sea" in line 22 with "be" in line 24. So it's all free, doing what it wants without even abiding by the perfect couplet form the poem opens with. Overall, we get the balance of the more classical conventions of poetry with the more imperfect and freer innovations of modern poetry. And in the end, none of it really matters once we understand that a poem, no matter what, must "be" instead of "mean."