The 73 240z I am working on makes "some hellacious noise" when I turn to the right. What should I be worried about? BTW the driver side boot is ripped. I am hoping new u-joints will solve the problem... is this wishful thinking?

Normal. The side gears and pinion gears inside all have a bit of lash, you're just feeling it through the halfshaft. If the halfshaft moved up and down a lot or the car made some hellacious noise when you turned, then you should be worried, but what you're describing is normal. Also normal to be able to twist the driveshaft a little bit before the halfshafts start to move.

The 73 240z I am working on makes "some hellacious noise" when I turn to the right. What should I be worried about?

Waking the neighbors? Hearing damage? Seriously, your words say little...

The boot keeps dirt out of the slip yoke. It's not a traditional slip yoke, almost like a CV shaft in the way it goes together with ball bearings in there.

I'd suggest you just find another good used halfshaft rather than fix the boot and replace the U-joints on the one that you have.

Diagnosing noises over the internet isn't always the easiest thing to do, but for a noise that happens when turning I'd look at wheel bearings and spider gears. U-joints typically make a clunking noise.