One would hope that all products labelled as non-toxic are in fact non-toxic. There is no easy cheap way to make such a test by yourself. Consumers must rely on government agencies to test products and enforce truth in marketing and labeling of products. In the USA, two major agencies responsible for this are the Food and Drug Agency (FDA) and the Federal Trade Commission (FTC). Other countries have similar bodies. At their websites you can find product alerts, recalls of toxic products, and much more.
There are different levels of toxicity, and there is a rating scale. The usual level at which a compound is considered toxic is called the LD50 which is based on testing things on rats. You keep giving the rats more and more of a substance, and you count how many die. The LD50 is the point where the "Lethal Dose" (LD) kills "50%" of the rats in the experiment. It's too bad rats have to die, but this is the classic way that toxicity is determined. You can never know for sure if a product that kills rats will also kill humans, but there's a very good chance it will. In general, products are called "Non-Toxic" and are allowed to be sold as such if they contain thousands or even millions of times less than the LD50 for a given compound.
For an overview of toxicology, the study of poisons, try Raymond Agius's website.