I'm a big fan of what I call "kitchen sink soup" - because you throw everything but the kitchen sink into it. Soup is pretty flexible, but it is still possible to mess it up.
Starchy ingredients, like noodles, barley or rice, absorb more water than you'd expect, and can suck up all the liquid, leaving you with a mushy stew rather than soup. Strong ingredients can dominate the flavour - think turnip, radish, or too much cabbage. Things like onion and celery can have an unpleasant texture if they aren't sauteed first. It's possible to over salt - particularly if you add salt at the beginning, and that's hard to correct. And, in general, if you throw too many random flavours together you can end up with something muddy tasting and not very appetizing.
So I might throw some leftover pesto chicken into a soup, and go with an Italian flavour profile - tomatoes, spinach, etc. Or I might add those sesame noodles, and adjust the seasonings to something more Asian, with a bit of soy sauce. But sesame noodles and pesto chicken wouldn't get thrown into the same soup.
Mashed potatoes might work, but if you just throw them in, they'll probably end up lumpy. I'd mix the potatoes with the broth, separately, blending until smooth, before adding to the chunky ingredients.