About the birth year, the 1920 census shows John age 16, and 1910 shows him age 6, which would be correct for an Oct 1903 birth. His younger sister Agnes is 3 on the 1910 census. I don't have his birth record in my files, but what you've got there isn't a birth record, it's the index of the 1930 census - and I do have a copy of the 1930 census record showing he's 23, but it conflicts with every other record - and all the Foley children's ages are listed wrong on that census, only their mother's is correct. I do have Agnes's birth record, and she was born Feb 23 1907 and christened Mar 10 1907 (I can send you a copy if you want, just let me know), so I don't believe John's year of birth could be 1907, since he was older than Agnes. There's a much bigger difference between 3/6 and 13/16 than between 23/26, so I'd think the younger censuses would be more accurate since the age would be more noticeable. The census is not always great as a primary source (in 1920, for example, Bridget is listed as Beatrice), and the 1930 one is a bit problematic in this case. Agnes is listed on the 1930 census as 20, when she should be 23. Teresa, who would be 28, is listed as 25, and James (known as Gentleman Jim), who would be 33, is 30. If you look at the family right above them, the Fahlbushes, that's the eldest daughter, Elizabeth, and her husband, living next to her widowed mother and single siblings - William and Elizabeth have three young children, and Elizabeth's age is also incorrectly given as 33 (she would have been 36 at that point in 1930). So either the Foley children all decided to freshen up their ages a bit, or whoever told the census-taker the family details did not remember correctly and subtracted 3 years from everyone's births (strange). On the 1930 census Joe Foley is married and has his own household, and his age is correctly given as 30 - the same as his three-years-older brother Gentleman Jim.
Do you have a copy of the original record of the marriage? Because Soundex indices are sometimes listed wrong, or someone mistypes or misreads. I spent days trawling through the 1900 Brooklyn census page by page looking for James and Bridget, because they weren't indexed - when I finally found them and looked closely at the record, the census-taker in 1900 had forgotten to cross his F, so it looked a bit like a T - they were indexed as "Toley". The Kennedy/Hennigan may be of a similar problem.
You'll find, on censuses particularly, that spelling, along with numbers in general, were a little more fluid in those days ;) It can be frustrating for genealogists when you're looking at four different sources with four different ages when you KNOW it's the same person (this has happened to me before, on my father's line, who apparently regarded birth years as optional). I tend to count birth/christening records as the most trustworthy, so long as they were recorded at the time of the event (most were, but there are exceptions). In this case, given the 1910 and 1920 censuses and Agnes Foley's birth record, I don't think a 1907 birth year is possible for John.
If he was born in October 1903 and his wife was born in 1906, that's not much difference in age. I have his marriage to Charlotte Sullivan on 10 Jun 1931 at St Mary's in Bayonne, but I don't have anything about Charlotte beyond that.
I'm waiting on a call from my mother - she is a nurse and works nights, and lives in a different time zone from me, so our phone call schedules often conflict - about the Kennedy thing. I'll ask her if she has a copy of the actual document for John Phillip Foley's birth or christening. It may be this evening before I get to post back, but I will!
I have the genealogy forums here set to email me a notification if I get a response to any of my posts, since I don't check here terribly often these days - it's handy that way, I always see replies straightaway. I have a bunch more information on the Foleys - your grandfather's siblings especially (9 of them in total), and his mother's siblings (Bridget Convey was the 5th of 7 children), if you want to swap email addresses. :) I keep all my data in a Legacy program file and my copies of the records scanned and sorted by surname on my hard drive - I've been doing genealogy about 15 years now, and my mother has been at it since about 1980, so between the two of us, it's a lot of information to keep straight. It really could be a full-time job!