I installed a new kitchen sink faucet into a kitchen with over 60 year old plumbing. I tightened the connections at the point where the rigid piping meets the flexible risers, and there was some dripping, but only 10 to 20 drops per hour. I tightened them as much as I dared; any more and I fear I would have risked damaging something.
I put cups under both connections. The cold has stopped dripping (or maybe it now drips so infrequently that the water in the cup evaporates before I can look at it). The cup under the hot has only 1 or 2 teaspoons of water in it after 3 days.
Need I be worried? I live in an area with very hard water and I suppose lime deposits are flowing out and have blocked/will block the hole. The hot pipe in particular had streaks of lime all over the pipe threads; I tried to clean it but didn't get very far.