I found this quite interesting (hat-tip: 3 Quarks Daily). It reminds me of the Shire Calendar in the appendices to LotR (with concession to our current calendar, of course). It would be annoying, though, for us Americans to have Fourth of July every year falling on Wednesday, an awkward day that is not conducive to four-day weekends. And that Newton week is not, I think, as convenient as a leap-day system.
If such a calendar were to go through, on the matter of birthdays would it be better to backtrack and convert your birthday into the new calendar day, or to carry over your birthday into the new calendar (or as close to it as possible)? If I keep August 7 in the new calendar, I will always celebrate my birthday on a Monday; which is actually the day I was born, but this is not so for everyone.
Henry, incidentally, has a Calendar Reform page. Rather than 'Newton' I would recommend that the week be called by the old Roman calendar name, "Intercalaris". Intercalaris was a month occasionally inserted after February before the Julian reform (which left only the leap day as a residue). From what I understand, it was also called "Mercedonius"; so perhaps 'Mercedon' would be easier on the ear. If it has to be named after anyone, it should be named after Clavius, who did most of the astronomical and mathematical work behind the Gregorian reform.
