The nastiest primate - for this discussion discounting a sadly rather significant proportion of the human species - I've ever encountered was a male chimpanzee named Jimmy at the Olmense Zoo in Belgium.
This chimpanzee apparently doesn't really enjoy being watched and sometimes shouted at or heckled by visitors, and he responds by throwing whatever he has at hand at visitors - chunks of grass, mud, sticks, rocks, food scraps, and worst of all, fecal matter.
There are signs explaining his behavior and advising visitors on how to behave near the chimpanzee exhibit, but unfortunately for some of the nastier members of our own species (and I'm putting this pretty mildly here) that just seems to have the opposite effect and seems to encourage them to do just the things the signs prohibit, i.e. shouting at the ape, imitating his intimidation displays and so on, which usually provokes the ape into throwing stuff. I've seen this happen at the zoo myself - after being heckled by an idiot visitor the ape threw faeces towards the public (I guess he had ran out of mud already). The steel mesh barrier and wall at the front of the exhibit, as well as nearby areas are often covered with the leftovers of the chimpanzee's behavior.
I've also seen chimpanzees throwing or smearing fecal matter on the windows in Antwerp, but at least they have no way of reaching the public.
I would say that anything involving primates, in this case chimpanzees, and their faeces would count as pretty nasty.