Margie,
By the 1880's, civil registration was the law throughout the entire Italian peninsula and, especially in smaller comuni, it is unlikely that someone slipped through the cracks.
Question: when you say you, " have been through the entire year of microfilm records", do you mean that you searched the indexes, or the actual individual birth acts? Many of us have had the experience of locating a birth, marriage, or death act which was not listed in the annual index - not surprising once you understand how these indexes were manually created at the end of the year.
As to, "I am certain of the place, even though the marriage certificate lists his birthplace as Campobasso. My aunt insists that my grandfather and his family never left Colle d'Anchise..." well, once again, it is amazing how often these oral family histories turn out to be wrong in both minor and major ways. So, do keep an open mind. As an example, if your great-grandmother was having a difficult pregnancy, she may have went to live with a relative or friend (or, though unlikely, a hospital) some distance from her home. If your grandfather was born in this other location, his birth would be registered there, not in Colle d'Anchise.
What happens if a woman gives birth and is not married? Is this still registered? I am juts trying to figure why I cannot find it.
I have several cases in my own family in which the birth record is in the mother's name, although they are all from much earlier in the 1800's. See this thread:
http://italiangenealogy.com/Forums/view ... 18975.html
Other threads of interest for their background material:
http://italiangenealogy.com/Forums/view ... 18885.html
http://italiangenealogy.com/Forums/view ... 19189.html