NewBDR,
I had a problem with the self-cancelling part, but not with a loose assembly. I did notice a few items that may help you while I was working on my steering wheel and turnsignal assembly. My set screw tightens up enough to hold the turnsignal in place without spinning.
Make sure that the turnsignal assembly is far enough back toward the dash so the set screw grabs the steering column. Also that the assembly will clear the rear of the streering wheel.
As for the self-cancelling part, I had to add an R/C airplane wheel collar to the strike pin on the steering wheel and add a little grease to the turnsignal arm behind the snap ring so it would return to neutral. There is a pic in my gallery of the wheel collar.
If you ever have to take apart the turnsignal assembly be VERY CAREFUL. There is a large spring and some sensor tabs that need to be put back into place very carefully with a small screwdriver. Its kinda tricky.
If davidlee's suggestion doesn't work, then you might try re-tapping threads to the next size and install new set screw. The assembly is aluminum, so use the proper thread locker.
HTH