No medication or supplement is tested for all of those things. There are guidelines on what safety protocols must be conducted with pharmaceutical medications (and the efficacy of these has been hotly debated, both on the choice of protocols, and who/how they are conducted). I'm not sure what the "implications" really are beyond that. There are far less safety protocols required of herbal and other non-traditional medications - in fact, there are hardly any regulations at all.
I can say that one of the reasons it's so hard to study all these effects on vaccines and other substances (plastics, food additives, herbal supplements) is that it's not just the substance itself that may or may not cause an effect, but the additive combination of a person's environmental exposures. It's also hard to design a study where you can follow someone long enough (again, under controlled conditions?) for an effect to present itself. It's impossible to control for this, and a huge question mark for the individual effects of substances on each person. The devil's often in the dose, after all. I would love to see stricter and more independently tested safety protocols on vaccines and other medications, though, if that's what you're looking for. I'd certainly like to see some regulation of "natural" medicines, to be sure.
Anyway, that's my two (rambly) cents.
