You miss the point -- if the disease protected against is rare, then the vaccine can easily be worse than the disease it cures if given to large populations.
Yeah I guess it could. I guess the vaccine could cause a unicorn to fly out of your butt too. But it didn't after five years so I think we are safe for now.
This isn't some crazy drug cocktail being put in your body, you know. It's just made out of proteins. Your body attacks, metabolizes and flushes it out within a few days. After that you're just left with some ass-kicking antibodies.