Connected a new faucet, the pipes drip but only a little bit, is that a problem?
It is a problem, and you should fix it because small leaks tend to become bigger leaks. You can't rely on hard water deposits to seal things, and drips can cause corrosion and damage to your kitchen. Even if it stays a slow drip you'll always have it at the back of your mind. This is a case where it pays to do it right at the beginning.
It sounds like you have crud on the threads, or maybe the threads are worn. If you want to use the existing threads then clean them off thoroughly, you can use an old toothbrush to start, and a wire brush if that doesn't work. Then use teflon plumbers tape or thread sealant.
If the threads are worn or damaged you're better off cutting the pipe a bit and then either re-threading them or using a push-on or compression fitting.