Polyurethane, like virtually all plastics is made of nitrogen, carbon, hydrogen and oxygen. So the byproducts are things like water, carbon dioxide, ammonia, alcohol.
Plastics burn really well, they are not actually that hard to destroy safely - their decomposition products are very clean if the fire is hot enough.
It's possible to burn polyurethane safely, but it's not trivial. If you burn it at low temperatures, you get hydrogen cyanide, and if you burn it (or, in air, anything) at high temperatures, you get deadly nitrogen dioxide instead. You can get rid of the nitrogen dioxide with sufficient effort; http://www.aat.cc/store.asp?pid=26808, for example, sells a six-stage air scrubber system using a sequence of strong oxidizing and reducing agents.
In short, "not actually that hard to destroy safely" is wildly off the mark.
Your other statement is wildly off the mark, too. Metabolic byproducts are incredibly diverse, including all of the chemical compounds produced in the course of an organism's life cycle. One of the organisms studied in this paper was Aspergillus niger, whose metabolism produces, among other things, aflatoxin. EDIT: Oops, WRONG. It's other Aspergillus species that produce aflatoxin, sorry. A. niger is mostly notable for producing 99% of the citric acid in your food.
I should also point out that there are plastics that are even harder than polyurethane to burn safely, namely, anything containing chlorine or fluorine. The common ones are polytetrafluoroethylene (Teflon) and poly(vinyl chloride) ("vinyl"). These, regardless of how you burn them, are going to produce compounds of fluorine and chlorine, typically gaseous hydrofluoric and hydrochloric acids, which will EAT YOUR FUCKING LUNGS. HF will also poison the fuck out of you. On the plus side, these gases are light and will disperse rapidly if they're not confined.
Nitrogen dioxide is a problem, but at an industrial scale it's not a huge problem. Among other things it can easily be captured with fractional distillation (water, CO2 and NO2 have very different boiling points), converted to nitric acid and sold.
And aflatoxin (and others) are not byproducts, they are deliberately made by the organism, regardless of what it eats. A byproduct is waste that depends on the food source.
Plastics burn really well, they are not actually that hard to destroy safely - their decomposition products are very clean if the fire is hot enough.