As a note, using waste as fuel was EXACTLY what the plains Indians did; since the plains region of the U.S. had very few (if any) trees, at least some tribes came up with the idea of drying buffalo waste and using it to fuel fires. That was pretty much the only thing they had to work with, and it worked quite well-keep in mind that what comes out is not 100% digested, especially in herbivores (you can actually find blades of grass or leaf pieces in their droppings). If implemented for LIVESTOCK, it would also give a good reason to actually set up a proper stable instead of just letting them wander around the fort.
It could also be converted into compost, which would give a place to put all those animal remains the cats bring you. Could also offer a solution of what to do with meat that gets rotten-ditto for withered plants. Put it all in a "compost" heap, and then use the result to fertilize. They still use cattle-and even human-feces to fertilize crops-the same ones we buy in the supermarket. And if works today, even when there are more sophisticated chemical-based fertilizers, it would almost be a necessity in medieval times. Where wood is scarce, every bit is a precious resource; if you can avoid burning wood to make potash, then you would do so. Using composted feces as fertilizer does just that.
Also, I do believe that livestock feces used to be mixed into mortar, at least some of the time-I could be wrong on that one. Once constructions become destructible, mortar and mortar strength might become a real issue, and this could have an effect on it. It would definitely be better than having no mortar at all. There is also the fact that decomposition does produce methane gas-which could build up to lethal concentrations if it gets trapped with no way to escape (incidentally, methane is odorless: they add hydrogen sulfide to give natural gas-that is, methane-an odor so you can tell when there's a leak). Much like gas pockets in mines, a methane explosion could occur if a heat source (flaming arrow, fire snake, imp, SoF) gets in contact with it.
As a poison, not so much-alcohol is a great disinfectant (in fact, natural production usually stops when it builds up to a high enough level to kill the yeast/microbes making it), so if the army brings along strong booze they might be able to mitigate the damage somewhat. Of course, given conditions in battlefield camps...that might not matter, they might die of an unrelated infection just from wounds caused by the trap.
I would actually say the management part is almost mandatory-as is, when a siege comes and I can't fight it off (read:crippled military and 40+ orcs), I just lock the doors and boom! I'm self sufficient for the season. Waste management would add a new dimension to that-if I need to manage waste and don't have a proper sewer system, then I NEED to find a way to deal with those orcs. This would also make aquifers even MORE challenging-microbes can contaminate an aquifer, though the spread is slower than with flowing surface or stagnant water. This would mean you would have to devise a management system that did NOT contaminate the aquifer in the long term...not just channel into it and make it your waste holder.Make obsidian water tunnels filled by a floodgate into the aquifer and drained by a floodgate into the river/pumped into the river...Really now, you could even incorporate it into a megaproject.
Contamination could also affect what fish you can catch in rivers. For instance, carp have a high tolerance for water contamination, and can deal with most levels of contamination-except when there's so much waste the water becomes almost completely depleted of oxygen. This means that as other fish are pushed out, carp can thrive. Other, like trout, NEED clean, high oxygen water or they can die-meaning less fish for you to catch. I'll post a more detailed post on this particular topic later, but you actually get gradients along which you'll find certain fish and other aquatic organism, directly dependent on the oxygen level of the water and contamination.