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.)
This is a very good question. In general, you can help yourself work through any confusion by trying to express the idea more precisely or in a slightly different way. I'll use each of your examples to explain this a bit further.
EX1: All lizards have a head width, but that isn't what you measured. You measured the different head widths of a group of lizards, or "the head widths of some lizards." I would at least add the "some", but perhaps it would be better to include the actual number.
EX2: You are talking about the growth rate of all birds, not, say, the growth rates of different species of birds.
EX3: Each of two populations has a mean height, therefore there are two mean heights. You are saying that the mean heights of these two populations are different.
EX4: Dogs have noses is correct, but this is a bit inconsistent. For example, dogs have a sixth sense that lets them know when someone is coming, and they have a nose for trouble. People have minds, but they have a combative streak. So, when you are talking about a shared characteristic of all dogs, you use the singular, but when you are talking about something that each dog has, you use the plural.
Best Answer
I usually hear plural come next: One and a half teaspoons of sugar, one-and-a-half pages of data, e.g.
Also, you can switch to a singular noun if you reword the phrase:
I found this usage note in Macmillan:
The last example shows two and a half, but the wording would be the same for one and a half:
✓ A 60-minute movie might last one and a half hours with commercials.
Incidentally, you can find many forums about this very issue simply by Googling "one and a half hours". Evidently, you're not the first person to wonder about this.
Moreover, some sources recommend using hyphens:
But this is a style issue, not a prescriptive one.
Here's where it might get tricky: when preceded by an article, and used as a compound adjective, you use a singular unit, not a plural one. Notice how the wording changes in this dialog: