Dwarven shit sounds like a crude idea. I don't like it at all.
Piss is too useful in this tech-frame to be implemented in a non-squick manner. There would just be more yammering about 'ooo, it's for tanning hides'. And jello, according to one thread.
HOWEVER: This is the extreme. There is a middle everyone who spent any time washing dishes is familiar with: greywater.
Prong 1:
Eating now produces a dirty dish, if a dish has been manufactured. This is like crafts, and can be made of stone, wood, or metal. Dwarves get unhappy without them. Dishes are washed at a SINK, which is fed by a dwarf with a bucket. Water is handled as it is currently, with buckets. One level of water is used, and one level of greywater is produced. Greywater is either drained directly below the sink, or can be hauled away with another bucket.
Prong 2:
Dwarves can bathe and wash clothes in a TUB. Two or three units of water are used, and two or three units of greywater are produced. SINKS and TUBS are like beds or chairs - they are community-used unless assigned to a dwarf. This also gets rid of the 10-year crust a dwarf tends to accumulate. Tubs are metal or stone.
Details:
The building holds up to 6 tiles of water before being declared FULL/CLOGGED, and being shut down. If the water building has been PLUGED, the greywater is contained inside and a task for hauling the water away. If it is UNPLUGGED, the greywater flows like normal water.
BALANCE:
Water evaporates or can be dumped manually for the first 30 dwarves or so without incident. From then on, things get muddy. Therefore, it is not an impediment to learning the game. It is something that comes into effect after you've learned enough to have fun. Water is automatically dumped in the nearest water source.
Technical Approach:
Perhaps a flag could be added to a tile of water, indicating if it is greywater or pure water. Can the functionality for stagnant water be reused here? Ultimately, an integer value could be used representing a concentration of filth. Dwarves will drink water with a purity of, say, ten. Washing something produces a stack of water with a filth of one or two thousand.
ALSO:
Lynch me, but I think water should not be drain-able from the edges of a map. Part of the Fun of dealing with greywater should be making some sort of system, large evaporation ponds, a 20 z-level pump system to the surface, bottomless pit, whatever works.
DUH:
You may link below to the half-dozen threads where someone had suggested this before, and why it won't work. Or, you can surprise me and discuss.
Super-awesome dozen-boston-creme-doughnuts-for-you level of awesomeness (or equivalent, perhaps you prefer maple?) for Toady:
Magma-warmed water produces a happy thought.