Ok I'll start by replacing the U-joint. I now see the "black crap" behind it in the picture. How do I determine what u-joint to buy? The online 2005 manual indicates a part number 4635. Looking that up with Ford parts gives me a u joint repair kit. (See photos).
I've also read about standard sizes such as 1310 and 1330. Not sure if that applies here or which size comes with my 2006 automatic.
I assume I should replace the U-joint at the other end too?

 

Is your driveshaft straight like the middle picture or does it have the carrier bearing near the center of the driveshaft? The picture on the right is the whole universal joint. I don't know why Ford would call it a repair kit but they do strange things. I'm not sure about the part number. Maybe call your local Ford dealer 'Parts' department and they will tell you the right one to buy.