At one time or another in your genealogical research, you will reach a point where you must send for a copy of a primary source record. Primary source records are records created at or near the time of a particular event. Birth, death, or marriage certificates are usually the first things to enter a researcher's mind in this regard. In addition to being termed primary source records, they are also categorized as vital records. However, they aren't the only primary source documents and, depending on where you are in your research, may not be the record of choice for a particular situation.
I recently saw a message thread on a genealogy website where a person was trying to decide whether to send for a birth certificate, death certificate, or social security application form. Some of the dates of birth did not match and the person was trying to decide which record would be the most accurate.
First of all, it is important to remember that any record is only as accurate as the person who provided the information for that record, and the person who physically recorded the information at time of the event. When considering which record you want to send for, I always recommend choosing the record that was most likely created by the ancestor you are researching, or by the parents of that ancestor. A birth record is much more likely to be accurate for birth information than a death record. Death certificates, extremely official documents, often contain errors. The person who provided the information may have been a son-in-law or daughter-in-law who wasn't fully familiar with the family history. I have even seen death records where information was provided by a "friend of the family." Maiden names and even places of birth for the deceased, as well as birth dates, can be wrong.
Having said that birth certificates are usually more accurate that death certificates, I need to add that even birth certificates can be wrong. Many births, particularly those that occurred at home, were recorded after the fact, usually when proof of age or citizenship was needed. In the early 1900s most births still occurred at home. A notation in the family Bible, or a letter to friends and family may have been the only record of a child's birth that actually was produced at or near the time of the event.
A primary source document that is almost always correct with regard to date of birth is the social security number application form. Prior to the 1970s, social security numbers were only needed for those who worked and for social security benefits. The form was completed by the applicant, who presumably knew their own date of birth. The form lists the name of the applicant's mother, and—most importantly—her maiden name. You'll also find the applicant's occupation, home address, and work address.
What all this boils down to is that when a social security number is available, and you are as sure as possible that the person is question is the ancestor you are researching, I recommend you send for a copy of the social security number application first. If you don't know the mother's maiden name, this form will provide it. If you do know the mother's maiden name, this form will provide you with written confirmation and that ever-needed documentation for your records.
Always remember that genealogy is about the preponderance of evidence. If a death certificate has one date of birth, and the social security application form and the family Bible has another—both of which match—then the preponderance of evidence points to the form and Bible, not that official death certificate.