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The vast majority of cookware sold in America is perfectly safe;
manufacturer's certainly don't want to risk liability by having constituents
that could leach into the food or water.
Having said that, in recent years, a number of controversies have come and gone (although there are always a few conspiracy type websites keeping even the absurd ones alive.
Compounds used in the manufacturer of Teflon is the latest controversy. Very often in producing commercial products, hazardous constituents are reacted to form a new material which is inert or nontoxic. An obvious illustration is hydrogen (the gas in the Hindenburg) and oxygen. When combined, they can explode. But the reaction produces water. Only water. Nothing else but pure, clean water.
It seems likely that Teflon, which is highly resistant to degradation, is like this.
Aluminum pots and pans have also been vilified some years ago, because research showed that some brain tissue from Alzheimer's victims had elevated levels of aluminum. Later research has consistently disproved any correlation between aluminum cookware and Alzheimer's.
Ancient Romans use cookware, goblets and cutlery made of lead. One theory is that the resultant brain damage from ingesting lead over time lead to the downfall of the Roman empire.
In recent times, various products made in the Third World have turned out to be dangerous. An unscrupulous cookware manufacturer in Mexico once made frying pans that included nuclear waste!
A number of toys have been made in China that included high levels of leachable forms of heavy metals. Pottery from many third world countries has poor glazing covering clays that contain arsenic and lead!
Some types of plastic are not suitable for a microwave, as they breakdown; whereas others are intended for microwave use.
Having said all this; if you wish to be as protective as possible of your family's health, sticking to tried and true cookware made of nontoxic metals, such as stainless steel; or glass (the heat resistant types!) that are manufactured in countries that have strict liability laws (such as the U.S. and E.U.) is the safest path!