Unfortunately, the subtitle of the book, "edited and mildly modernized" is too mildly stated! It is heavily modernized. It's one thing to remove some of the thees and thous, especially from the prose sections, but it goes much further than that. In the poetry section, it restructures sentences and changes words so that poems that ought to rhyme, no longer do. For sonnets, that's horrible since the rhyme structure is critical to the sonnet form of Donne.
And there are editing mistakes. For example, on the very first poem, "The Crown", there is an entire line missing (the second to last line). And #4, "The Temple", has an extra line (lines 7 & 8 should be one line, but it's been butchered into two lines that throw off the sonnet).
Also, Donne's poems have great emotional intensity. Somehow these modernizations manage to suppress that intensity and make them pretty mellow. That's really too bad.
It's a nice attempt, but it just doesn't work.