Medical student and amateur historian here. There are two classic examples of mistakes by the pharmaceutical industry that lead to major reforms of the FDA. One of them I will talk about here pertains to the drug elixir sulfanilamide and the other which still may be of interest to you is thalidomide.
In the United States the Food, Drug, and Cosmetic Act of 1938 was the first legislation of its kind requiring new drugs to undergo a pre-market evaluation for safety. This mandated that the FDA review the results of clinical (human) and pre-clinincal (animal) trials.
This 1938 act was in response to the 1937 release of a drug called elixir sulfanilamide. This drug is essentially the antibiotic sulfanilamide in the solvent, diethylene glycol. Diehtylene glycol is now know to be toxic but was not know at the time. There were no animal trials done on the drug prior to testing on humans and its release publicly.
There were over 100 deaths as a result of its release. If the rigorous testing that is done today were performed on elixir sulfanilamide it would have never been approved.
Sources:
"Deaths Following Elixir Of Sulfanilamide-Massengill." Journal of the American Medical Association 109.17 (1937): 1367. Web.
"Elixirs, Diluents, and the Passage the 1938 Federal Food, Drug and Cosmetic Act." Journal of Occupational & Environmental Medicine 38.7 (1996): 661. Web.
The classic example here is thalidomide. According to this article from the Journal of Philosophy, Science, and Law, animal testing was common at the time in West Germany (where Thalidomide was developed), including teratogenicity testing (testing for congenital abnormalities). But, the records of the scientists who developed thalidomide were destroyed, so we cannot say for certain if the drug was tested on animals or not, although it seems likely. Regardless, however, it appears that even if it had been tested, that would not have necessarily prevented the disaster, as subsequent tests have shown. Apparently many animals, rats and rabbits among them, do not exhibit the same effects from thalidomide that humans do.
Edit: words