For example, husbands and wives often do not know the maiden name of their mother-in-law, and on their spouse's death certificate they often guess — wrongly.  Ditto the in-law's places of birth.  (Before you got interested in genealogy, did you actually know where your mother-in-law was born?)  Not to mention that the informant is often in a state of shock and grieving (i.e., not functioning at their best, especially intellectually).

One of my great-uncles was the informant on his mother's death certificate and on those of two of his siblings.  He gave a different place of birth for their mother on each certificate, and all three of them were wrong — and all three of which are preserved in the LDS International Genealogical Index online at FamilySearch.org.

One of my uncles — an attorney, no less — on his wife's death certificate gave the wrong maiden for his wife's mother.  The name he gave was a prominent one in the family, so I understand why that name came to mind, but it was not his mother-in-law's maiden name.  (It was, in fact, his mother-in-law's maternal grandmother's maiden name — that's how far off he was.)

And I can now add myself as contributing to this problem.  My father was born 11 Nov 1918 (the original Armistice Day).  When he died, I filled out the information for his death certificate at the funeral parlor, and I was a basket case at the time (utterly grief-stricken).  Instead of 11/11/18, I accidentally filled in his birthdate as 11/18/18, so his death certificate is wrong as to his birth date.  It is also wrong as to his death date.  He died at home on the evening of Easter Sunday, 16 Apr 2006.  The coronor was not notified until the next morning, so his death certificate shows his date of death as Monday, 17 Apr 2006.

[By the way, the "military style" of reporting dates (e.g., 18 Nov 1918) has been shown to be the format least likely to result in errors, which is why the military adopted it as its standard.]

Beware especially of birth dates of women on death certificates.  Many women are lying about their age in mid-life, especially widows and other women with multiple marriages, so their informant will unintentionally give a wrong birth year.  They'll get the day and month right, because the birthday was undoubtedly celebrated in the family over the years, but always suspect that a woman's birth year may have been earlier.  My mother married second to a younger man and lied about her age to him — and everywhere else she needed to in order to hide her true age.  This included her Marriage License, Driver's License, and Social Security application.  She was a rural home birth, so has no birth certificate.  I only know her real birth date because she confided it to me after I became an adult (and only then because I was filling out a passport application, and she didn't want me to have a problem with it by giving the wrong birthdate for my mother).  It isn't just women who shave years off their age in mid-life.  Men do it, too, especially widowers looking to re-marry.

An opposite problem with death certificates is "age-inflation."  While people may try to appear younger in mid-life, once people become elderly, they become proud of how long they've lived.  The elderly tend to exaggerate their age, and the older they are, the more likely they are to exaggerate.  It is not unusual to find someone in their eighties claiming to be in their nineties.

You will sometimes find that the informant on a death certificate is the deceased!  How this seeming impossibility can occur is that the individual has pre-arranged for their own funeral and disposition, supplying the funeral home with the information needed for the death certificate — except for the date of death, presumably! 

Despite the inherent fallibility of death certificates, if you have kin who died after about 1910 in the United States, there is probably a death certificate on file with the county or the state, and these are worth getting — and get them soon!  Some states have clamped down on who can get vital records, and more states are sure to follow.  I recently tried to get a death certificate for my first cousin from the State of Alaska and was refused.  Alaska does not release death certificates, except to immediate next of kin, until 50 years after the date of death.

A good online site for centralized information on where to get vital records is Vital Records Information.  Also, many USGenWeb county sites have information on how to get vital records in their county.

The problem of a "misinformed informant" also applies to tombstones because the data on the stone depend on the knowledge of the person ordering the stone.  The danger of error is much greater when the tombstone is placed years later — often by a descendant doing the family genealogy.

There is also the problem of the misreading of stones.  As stones erode, they become increasingly difficult to read accurately.  Don't depend entirely on someone else's reading of a stone, and be prepared to accept the fact that a stone simply cannot be read.

As with most historical and genealogical records, death certificates and tombstones cannot necessarily be treated as absolute fact.  Everything is true to one degree or another, and the more evidence you can gather, the more confidence you can have that you are nearer to "getting it right."