[Kadric]

Don't forget most of the inner circle were related. DNA if not Saddam's will not prove it is Saddam Unless we can get it from a son and daughter(preferably from the same mother). The daughter will give X and the son will give the Y.

[Tree of Liberty]

All his children are reportedly from the same mother (a 2nd cousin, I believe)

[Diddle E. Squat]

They can take samples from clothing, personal artifacts(combs, etc.) in Saddam's palaces, see if one stands out as recurring most frequently, to get a likely match on Saddam's DNA.

[JLS]

Your mitochondrial DNA is passed down the same from mother to child. So if you have to people with an unbroken chain from the same female, say the same grandmother like cousins, their mitochondrial DNA would be the same. This is true even when the last person is a male.

I learned about this on the history channel bit about digging up Jesse James. They compared the mitochondrial DNA of the body to someone else in a direct female line [actually two] from Jesse James' mother. Their mitochondrial DNA was the same leading to the conclusion that body in the grave was a direct descendent of Jesse James' mother.