To me the use of "feces has" and "feces have" are both valid, and do have distinct implications, which are based on your "mass noun" instinct.
If you write "canine feces has the potential" then you are talking about canine feces in the abstract, uncountable sense; you are attributing to it a particular property that it has due to the basic fact that it is canine feces. (For example, dogs may have some bacteria in their intestine that can also infect humans, and some of this bacteria is always present on their feces; thus canine feces has [by its nature] the potential to cause a health problem. )
If you write "canine feces have the potential" then you are talking about feces in the concrete, countable sense: that is, you are saying that the problem occurs because of the quantity of feces that is present. (For example, the aforementioned bacteria might only infect a human who comes within a foot of the particular turd upon which it resides; thus canine feces have [by their presence in quantity] the potential to cause a health problem.)