There's quite a few English (and other) translations of the Hyakunin Isshu. This stems from the fact that we are talking about a very classical anthology of Japanese Literature and that it is reasonably small (100 poems, and being waka poems, quite small at that).
The Hyakunin Isshu was compiled at the beginning of the 13th century as a kind of private collection, thought to decorate with it the walls of his rural mansion at Ogura, by one of the greatest of Japanese poets: Fujiwara no Teika (a noted poet and compiler of anthologies, among them the Shinkokinshu and the Shinchokusenshu). Much later, it would become a very popular text, a staple book for the Japanese of lower classes when studying the old waka poetry tradition (which always remained quite elitist and aristocratically oriented) or for women's education. The more noted printers of the Edo period and later would make nice editions with drawings of the poets and the poems, including also extensive commentaries in the editions with different interpretations of the poems and their arcane images and language.
So... Why is Mostow's edition so good? It includes the poems in carefully made translations. It includes pictures from different books (and even kimono patterns), explaining why the images are not just 'illustrations' of the text and act as 'pictorializations' (they create and independent and proper iconic language with pictorial metaphors for their textual equivalent, and they sort out and choose their images among different possibilities reflected in the criticism). And it also includes comments with biographical information on the poets and the interpretations of each poem.
Overall, this is a delightful edition of the Hyakunin Isshu, which merges good scholarship and nice reading qualities. I heartily recommend it.