I've read to never use detergent on a moka pot. But I've never tried it to find out! I find that simply using my fingers to brush it clean under warm water after each use seems to work just fine.
Yeah I just wash it with hot water. If I'm using it in the afternoon having made a morning coffee a few hours before, I'll just use my fingers. In the evening I'll clean it a bit more carefully, with a sponge or whatever I have.
Once I was curious if I was using my moka pot "wrong" so I checked some videos on YouTube and some of the people had immaculate Mokas. Like mine are clean, but these were near mirror-finish polished even though they'd been used.
Since most Moka appear to be made of aluminum, you would not want to put in a dishwasher (too caustic). But dish soap of the normal variety should not be a problem?
I put a disassembled one in the dishwasher once, there's actually a bit of lubricant on the threads that a dishwasher will clean away and it's not the same again