What health problems does polyurethane cause?

Inhaling it . Can cause irreversible lung disease .
Questions toxicity. Toxicity of any substance depends on a number of factors, not the least of which include: route & form of administration, amount consumed, & other medical predispositions. With polyurethane, there may be adverse effects on the respiratory tract, vascular system, & reproduction, to name a few. I encourage you to search websites like pubmed to learn more. If questions, avoidance is a good plan.