Not only did I not get the faucet clean, but I broke the entire faucet. Then I tried to install the new one and failed at that too. After hours of wasting my own unskilled labor as well as several of the husband's, we ended up calling a plumber in the end. So that's the short version. If you care to hear the whole story, keep reading.
When I tried to tie the bag of vinegar to the faucet, it just plain didn't work. I couldn't get it sealed, so the vinegar kept leaking out of the bag and running down the underside of the faucet. After several attempts I gave up. I also realized I could hear a dripping sound under the sink. Somehow, and nobody knows how the some is, the vinegar was getting from the sink into the cabinet below. Of course I was frustrated and knew I'd have to chase that problem down, but first I was determined to get that aerator clean!
I figured I could unscrew the aerator with my hand. Nope. So I grabbed some pliers. Nope. The crust had gotten so thick that the aerator was stuck tight. Then I remembered my brother gave us a vice grip. Awesome! A chance to use it, right? Yeah. Rather than working through the green and white mineral deposits, I ripped the faucet in two. Seriously. I'm not that strong. I don't know how it happened. I would guess that it was cracking already which is how the vinegar was getting through. It's too bad nobody got to see the look of horror on my face when I realized what I had done.
Off to Home Depot I went to pick out a new faucet. I talked to friends, watched online videos, and read how-to articles. With a little more help from the vice grip (apparently I didn't learn my lesson after the first incident), I finally got it installed! And it was leaking. The husband and I tried and tried to fix the leaks. My mother-in-law gave me some great tips but sadly I still had one last leak we couldn't figure out. We just had to call a plumber.