Shouldn’t the positions of National Security Advisor and Sec of Defense be filled by retired Generals or someone with extensive military background. Rice has no military background and Rumsfeld was a Navy pilot. Hardly a lifetime of learning what it takes to defend a country. I know these are executive positions; am I missing something about the role these people play?
You’re missing the fact that they’re executive positions. 
Even though you acknowledge it, you haven’t assimilated it. “Good executives know how to delegate”. Rumsfeld doesn’t need to know how to “make war”, all he needs to know is how to delegate “making war”. Which he has done, to Tommy Franks.
Ditto Rice. She doesn’t need to know anything about “national security”, just how to pick people who do know.
Also they’re both political appointments, and political appointees sometimes have no gloves-off experience of the Cabinet post they’re expected to fill. Ann Veneman may be an exception in that she actually grew up on a farm, but Spencer Abraham had no particular experience with “Energy”–he’s a career politician, a former law professor and lawyer.
Regarding the Secretary of Defense, there’s also the argument that having a retired General in that position would detract from the idea that the military in the U.S. is under civilian control. To preserve the principle that the military isn’t an independent political force (as it is in so many other countries, particularly in the third world), it’s helpful to have a civilian calling the shots.
The heavy military experience is well-represented enough by the Joint Chiefs of Staff.