That kind of testing will catch impurities, insecticides, and other contaminants.

It will not, however, identify levels of active ingredient in most cases where it isn't known.

It will not detect toxic byproducts of herb metabolism. For example in the 80's L-tryptophane was used as a sleep aid. As an amino acid, one would expect it to be a safe product. It was linked to a disease called "eosinophilia myalgia syndrome". Later the causative agent was found to be 1,1' - ethylidenebis a byproduct of bacterial fermentation used in the processing.

Another supplement, 5-hydroxytryptophan, has been linked to a similar syndrome. They found an oxidation product in the supplement that has identical properties to a neurotoxin.

A similar syndrome was found in contaminated rapeseed oil in Spain during the 1980's.

Hepatotoxicity may be the most frequent adverse reaction to herbal remedies. Some of the more frequently reported offending herbs include Chinese remedies and teas (Jin Bu Huan, Ma-Huang), germander, valerian, mistletoe, skullcap, chaparral, comfrey, and herbal teas containing toxic alkaloids, pennyroyal oil, and kava. Although frequently transient, cases of chronic liver disease and acute liver failure have been described.

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Herbal

The toxic alkaloids mentioned above are listed here:
Pyrrolizidine