Oldmexico,
After reviewing your pictures, I believe that the shaky steering has something to do with that very impressive hood ornament!
I know I'd have trouble keeping it steady.
I would definately check the u-joints in your steering linkage, If you have a lose set screw, it could be dangerous. What kind of steering rack do you have? My car has an MGB steering rack (just like the original Cobras) that has shims that can be removed to tighten up the play between the pinion and the rack. If you can give more information about the car, someone here may be able to help.
Paul