Heck, all I do is take the MLT out on the back porch and spray it out with the garden hose after dumping the grains out. I don't even dissasemble it, just spray out all the stray grains out of the screen. When I used a manifold, I would take that apart though. Do it ASAP after the mash, before the sugars dry.
Then I store it in the beer room with the lid off and upside down. I do include the MLT in my periodic scorched earth total equipment cleansing. This is when I put every single piece of my brewery in the bath tub with a ton of bleach over night. At the same time, I go through my lagering fridge and fermentation freezer with bleach as well.
IMHO, the biggest danger with the MLT is letting mildew or mold take hold that could result in an off flavor, or be a source for later cross contamination of other equipment through accidental contact......so never ever store it with the lid on and sealed, unless you are completely certain it is dried......and even then I would avoid it if possible or at least put a mesh bag of salt and rice/beans or a dessicant in it.