I actually just spent last night cleaning out my big mealworm bin. I lead such an exciting life.
What I did was use plastic tweezers (or you could use regular metal ones, or chopsticks) to pick out all of the mealworms and put them in another container. I don't mind touching them, but the container was full of icky, dead mealworms and beetles. Double checked through all of the poop and then just tossed all the gross stuff into a plastic bag, tied and threw it away. For moisture I use carrots instead of potato, it's easier for me to toss a baby carrot or two into their container for them and they usually last at least a couple days.