Did you know that it is "Down syndrome" not "Down's syndrome?" It is a pretty common mistake, one I too made shortly after Charlotte was born. I think my first google search that Thursday night we got home from the hospital was for "Down's syndrome." However, I quickly learned that Down syndrome was named after the man who discovered it, John Langdon Down in 1866. Because the syndrome was named after him, and doesn't belong to him the possessive " 's " is not needed and not grammatically correct. It is also proper grammar to capatalize the "D" in Down, because it is a name, and not the "s" in syndrome.
Since learning this, it is amazing to me how many medical forms are incorrect. Just last week I was filling out a health history at the dentist for Katherine, and even though for her I don't check the box for Down syndrome, I still made a point to cross off the incorrect " 's."
This is also why it is incorrect to say that someone has Down's. Instead, simply say they have Down syndrome, or if you really must shorten it, you can say they have Down.