The problem with vitamin supplements is mostly related to free radicals, which are atoms with an odd number of electrons that form when the body turns food into energy. If they interact with DNA, then, scientifically speaking, you've bought yourself two front-row tickets to the shit show. Antioxidants, which you find in vitamins, are thought to combat this. However, when you take too many antioxidants, you kill too many free radicals, severely impairing your immune system in the process. Going nuts with vitamins to supplement your diet is like setting fire to the bar in order to stop a fistfight; sure, it works, but it's generally not worth it in the long run.
Not that you're any safer if you pay attention to the dosage. The FDA has virtually no oversight when it comes to supplements. Sure, manufacturers need to have scientific evidence in support of any claims they make, but they are under no obligation to present said evidence to the FDA until something goes terrifyingly wrong. And sometimes it does: The FDA recalled 237 supplements from stores between 2004-2012 because they contained substances that might cause death or serious injury.