Two cases in point: 1. My grandmother's death certificate. She died in 1960. I didn't even start doing genealogy until in the mid-eighties. I believe it was in the 90's when I sent off for her certificate. Right away I found several errors on the document. I wrote to the state of New York to see if it would be possible to makes any changes. One was regarding her name. They said if I could provide three sources or examples they would change it. I was surprised and pleased that I was able to do so. And the examples/sources didn't have to be real strigent. I had a paper item (ephemera) with her name on it that I was able to include to prove her correct name (plus others). [If you find yourself in this situation, it's usually not hard to get the mistakes corrected.]
2. My mother's death certificate - there were five errors on her document. And my father gave the information. Some of it I was surprised was wrong because I was sure he knew the right information. But my father was hard of hearing and (as we humans are) sometimes don't want to admit he didn't hear you - or thinks he did and gives an answer according to what he thinks you asked! However, I was able to correct these errors also. One was asking for her occupation and dad gave them his! He also gave the wrong name for his mother-in-law. And I KNOW he knew how it was correctly. So take anything and everything with a grain of salt. [If you are in a position to provide documentation to correct errors, do so!]
This is not meant to down grade official documents, by any means. They are important to have. But the more sources you have the closer you'll come to finding which piece of information is correct. The document closest to the event usually carries more weight then others. For example a death certificate with a birth date is less 'official' (trustworthy?) than the birth certificate of the birth date. BTW, census are another very good example of finding conflicting information. A man may age 10 years, but the women only 6 or 2! So, search all of them out including official government documents. Yet nothing is 'written in stone,' (and that includes grave markers) except the Ten Commandments!
Happy Ghost Busting!