[wiredgeorge]

Would seem like a good idea to get under the sink and tighten the connections to the spigots. On my kitchen sink, they were so loose they were slightly dripping when I got it. I believe they are plastic and just a snug with some channel locks did the trick. My drain has a large nut that keeps the plumbing tight under the sink and it was very loose as well.

Is your outside faucet part of the plumbing on the inside under the sink?