Snarky reply: You've sequences every single one of those cells and confirm that the DNA all matches?
Non-snarky reply: There is a huge difference between phenotype stability and genotype stability. Take 100 cells from your body and you'll find hundreds if not thousands of genetic differences between them (single mutations).
There are 3 billion base pairs in each copy of human DNA. Looks like only ~60 of them change from one generation to the next. http://www.nytimes.com/2010/03/11/health/research/11gene.htm... Just making the 4 trillion cells in my body means that each would have to be copied an average of 41-42 times. Probably some cells get replaced more often and others have a shorter path, so I'm not sure how many times DNA is duplicated before it gets to human reproduction. But going with averages: 41 * 3,000,000,000 / 60 means 2,050,000,000 copies per error. That's a few orders of magnitude worse than a modern hard drive but not exactly shabby.
The comment that spurred my comment concerned the stability of DNA.
You have to remember that offspring are only going to have the best DNA passed down to them, since many mutations would result in non-functioning gametes or non-viable offspring.
The best example I can think of spermatozoa production. DNA is copied in that process and a large % of spermatozoa are non-functional.
I know. If a germ cell has DNA that has been copied 41 times (the average that I calculated), and that DNA has accumulated 60 errors, that means 1 error per 2 billion base pairs copied.
Non-snarky reply: There is a huge difference between phenotype stability and genotype stability. Take 100 cells from your body and you'll find hundreds if not thousands of genetic differences between them (single mutations).