I take my keggles apart and scrub them immediately after using them for mashing. Unless you want to use tons of chemicals, stuff gets stuck in every little piece of your spigot, false bottom, etc. I used to only take them apart once in a while, but I saw more and more crud getting built up.
I left some grains in my cooler mash tun for a week. It took another two weeks of cleaning with chemicals to get that smell out.
I clean my cooler mash tun right after use (well all but one time... eww) but there might be a few grains left when I'm done. Generally I don't put the lid back on the mash tun, I leave it slightly off so that the inside can dry. As long as it isn't wet it doesn't start to ferment. I then give it another rinse before doughing in.
I brewed two weekends ago, but but was sick and put off cleaning the MLT until a few days ago. Luckily the weather has been freezing at night, so when I dumped it out it came out in a solid block. So far the dogs have not bothered it, but I expect the field mice to have a feast on the compost pile.