It's not dripping. It's just that when sticking the edges of a paper towel
under the crevice of the PVC connection nut, the edges of the towel are
getting slightly wet. Presumably this means it is leaking slightly, or do I
only need need to worry if I see a drip or see water running down the pipe?

J

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.