In many countries vaccines will only be licenced after rigorous safety testing and extensive clinical trials. Those clinical trials will usually include thousands of participants. After a new vaccine is introduced, it will continue to be monitored.

It's simply not true that "Vaccine makers can literally solubilize dog shit and call it a vaccine."

This information site from Oxford University provides an excellent summary of how vaccines are tested, licensed and monitored in the UK. The process is probably similar in many other countries:

http://vk.ovg.ox.ac.uk/vaccine-development