jaynews wrote:
I bought a whole new connection pipe and installed it. I went with PVC.
(The cracked nut on the old connection pipe was permanently attached. )

The new connection pipe is working. HOWEVER, I've been checking for TINY
leaks by sticking edges of paper towels around the edges of the nut at the
connection. KEY QUESTION: Should I have ZERO tolerance for the paper towel
showing any sign of wetness when I do this or is a slight bit of wetness
considered acceptable. I've already gone beyond hand tightening, and I
don't want to wind up cracking the nut and having the same problem as
before.

You don't say whether it actually leaks or not. In my opinion you
absolutely must have zero tolerance for any type of water leak. It
should not and must not leak. Pipes sometimes sweat though and this
must not be confused with a leak. You should use pipe tape or dope on
the thread to prevent leaks, that's the ticket.