Before we can discuss the techniques that Elizabeth Bishop uses to reinforce her theme, we must realize her poems rarely have an easy moral or a clear "meaning." What Bishop's poems do have--and "The Sandpiper" is no exception--is precise description of the physical world. What does it all mean? In this case, it may just mean that we are all like the sandpiper: "preoccupied, / looking for something, something, something."
Both the meter and the rhyme of the poem are regular, but not absolutely symmetrical.
The lines of the poem are roughly 10 syllables long, but some are as short as 7 and others as long as 12.
Some of the lines are iambic (a series of unstressed then stressed syllables):
of interrupting water comes and goes.
Other lines, however, are strongly trochaic (stressed then unstressed):
something, something, something.
The rhyme scheme shifts subtly from stanza to stanza. Stanza 1 is ABCA: granted, shake, awkward, Blake. So is stanza 3: them, drains, runs, grains.
Stanza 2, however, is even more symmetrical; it is a "perfect" ABAB: sheet, goes, feet, toes. The final stanza, though, doesn't truly rhyme it all, unless we bend "obsessed" to rhyme with "amethyst."
Perhaps all this "near-symmetry" is part of Bishop's description of nature. It is beautiful, there are discernible patterns, but there are also curved edges, protusions, peculiarities. One will never cease looking for "something, something, something."