Good evening, Penny,
I'm in the process of finding all the RANDAZZOS and TERRANELLAS mentioned in the birth records, and I hope to make my results available in some form to everybody who is interested.
Fortunately, the Family History Library has digitized this particular microfilm; if you have access to the site (which is free), you can find Giuseppe's birth record as entry 37 in image #322 (here's the link: https://familysearch.org/pal:/MM9.3.1/TH-1951-32358-22801-69...
) Unfortunately, the record doesn't indicate much, other than that Salvatore was a "villico" (farmer), age 30, and Lucia may have been 26 (it's hard to read).
Santo's birth falls in the years 1881-1884, for which the records don't seem to exist.
Interestingly, Salvatore and Lucia had a son Ignazio RANDAZZO, who was born on March 14, 1888. His record is number 18 in image 678 (here's the link: https://familysearch.org/pal:/MM9.3.1/TH-1942-32358-22867-28...
The only additional information is Lucia's declaration of a non-civil marriage (I have yet to determine if this means having had only a marriage ceremony in a church, or of not having been married at all).
I checked the birth records for the date of Anthony's birth, but there was no one of that name (or Eduardo).
After I complete the birth records, I'll start through the marriage records, which may be more helpful.