You can improve the coffee from a Moka pot massively by doing two things:
1. Grinding the coffee yourself just before you brew.
2. Put hot water in the base, rather than cold.
Then set a moderate heat. When the coffee starts coming out, gradually turn the heat down to maintain the flow rate. Take it completely off the heat before it starts to splutter, and pour straight away. There will be some water left in the bottom of the pot - don't worry about it. If you want a longer coffee top up from the kettle.
To see why you should take it off before it splutters, when you've poured the coffee, put it back on the hob until all the water has come out. Have a look and smell of the "coffee" and decide whether you want to drink it or. If you do, you will discover it is very thin and very bitter. It's this last bit of coffee that makes people think Moka coffee is usually bitter.
Erm, I'm not obsessive, honest!
Edit: and, as Roger says, don't wash it with soap. Just rinse it under the tap and allow to dry.