This poem is a mouthful! The first two lines are hard to say without sounding like you have a mouth packed with marbles. There's a lot going on in many of these lines – some are super long and chock-full of syllables. Others are short and direct. This creates contrast, and really sets off the short, usually declarative lines. Think of listening to the sound of running water for a while, then all the sudden someone bangs a pot against the wall! For example, in the fifth stanza we have these two really syllabically tight lines, "my Tudor Ford climbed the hill's skull" and, "where the graveyard shelves on the town." But the last line of the stanza is the short, "My mind's not right." This switching from long, descriptive, and poetic language to the simple declaration make those declarations stand out big time. Also, these fluctuations between long and short, poetic and plain, mimic the restlessness and unpredictability of the speaker's mind.
Then there's the rhyme. It's doing much the same thing as what the short vs. long lines is doing. Rhyme is present throughout the poem, but it doesn't follow a predictable pattern! It's like Lowell was trying to show us how this poem (like our fragile speaker) is trying so desperately to keep it together, but just keeps going off the rails a bit. Very clever!