I just cite the FDA's EUA. This is literally trusting the government and yet I'm still called an anti-vax conspiracy theorist. The following text comes straight from the Pfizer EUA published by the FDA.

The Pfizer-BioNTech COVID-19 Vaccine is an unapproved vaccine that may prevent COVID-19. There is no FDA-approved vaccine to prevent COVID-19.

Oh, and you may have a severe allergic reaction, or something unknown since it's still being studied....

Signs of a severe allergic reaction can include: • Difficulty breathing • Swelling of your face and throat • A fast heartbeat • A bad rash all over your body • Dizziness and weakness These may not be all the possible side effects of the Pfizer-BioNTech COVID-19 Vaccine. Serious and unexpected side effects may occur. Pfizer-BioNTech COVID-19 Vaccine is still being studied in clinical trials.

The simian 40 virus is a much scarier and relevant example IMO. Jumped species during the first polio vaccine, present in 70-85% of tumors in some studies and it's seldom talked about.

Thalidomide is an example of isolating the wrong isotope that ostensibly, wasn't well understood at the time.

EDIT: Another good vaccine example. https://www.bbc.com/future/article/20200918-the-fiasco-of-the-us-swine-flu-affair-of-1976