For the refrigerator in-door dish I just poured a little vinegar in the dish and let it sit for about 20 minutes. I took an old toothbrush and the hard water just wiped off without any scrubbing.
To clean my faucets I had to get a little more creative. I soaked some paper towels in vinegar and placed them on the areas with hard water. I took a spray bottle filled with vinegar and sprayed the towels every time I walked past. After about 20 minutes I took the towels off and scrubbed off the hard water with an old toothbrush. Some areas had thick hard water and I had to put the towels back on and wait another hour and repeat. I didn't have to scrub really hard, the hard water came off easily after soaking in vinegar.