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I have contacted Family Search about their N.H. Vital Records. They say that they plan to fix the errors at a later date.
I'm sure they were copied from the index cards at the State Archives in Concord.
The early NH vital records were recorded on the town level. Many, if not most, are intermixed with the town records. You can contact the individual town clerks to try for this information. There is a substantial collection of microfilmed town records located at the New Hampshire State Library in Concord. I have used these for some of my families with good results.
Also, church records can be informative, but I have less experience with them, than I do with the town records.