i use the same pot for brewing beer as i use for making soup, and boiling noodles, and pretty much everything else that happens in the kitchen.
all i do is wash it with dish soap and water, and make sure to rinse it out well.
i'm about 99% sure you could just run it through the dish washer, too, if it were to fit.
remember that the pot doesn't need to be sanitized, because you are boiling everything that goes into it. you only need sanitizer AFTER the boil.
and, if your SWMBO is anything like mine, she would be mortally offended to hear you talking about "foreign matter" left on her cooking pots and pans. my bet is that pot is as clean is you need it right now.
one thing i DO, however, is that i sanitize the lid during the boil so that when it goes on top of the pot during cooling it's safe.