Remember the purpose of the record when analyzing the information it contains. A birth certificate really is about the birth and minor errors in where the mother was born (if the certificate even contains that information) might not have been considered material. A probate judge was concerned that a person was dead and that probate proceedings should start, but might not be overly worried about the person's precise date of death.
A census was to count people and provide other certain statistical information for the government. The enumerator might not have been overly concerned if occasionally he confused a few children with step-children.