A less dramatic but still significant consequence of the Great Vowel Shift is that many poems from earlier centuries don't rhyme like they used to. End rhyme in poems rests in the vowels, after all, and when those vowels change, the rhymes are often thrown off.
In a challenging textbook and workbook on the history of the English language, C.M. Millward discusses and presents exercises on using rhyming couplets from older poems to determine how words were probably once pronounced.
I don't have an example on hand, but I can make up one of my own to illustrate. Here are two lines from my imaginary poem:
He washed and dressed his best,
To look as he should at the feast.
If this poet is any good at rhyming, we might be surprised to see the poem try to rhyme "best" with "feast." Those two words don't rhyme today. The chances are good, however, that these words rhymed in the past (around, say, 1500 or so): "best" was pronounced as it is today, but "feast" was pronounced as if it were spelled "fest."
The link below briefly discusses this use of rhyming couplets to determine pronounciations long before sound recordings were possible.
The Great Vowel Shift occurred over a period of time during the fifteenth through the eighteenth centuries. The shift happened at first in southern England but then spread.
During this shift, the pronunciation of English vowels changed. For example, the vowel in "feet" used to be pronounced more like the vowel in "fate." During the Shift, this changed.
The major consequence of the shift is that English has really weirdly spelled words. This is because the Shift occurred after printing presses had been invented. Spellings were preserved because they were already widely used in print, but pronunciations changed. That is why our words are not spelled phonetically.