Most of those scary chemicals on that diet soda's ingredients list are harmless, aside from the phosphoric acid (which is in regular soda as well) if you're in a high-risk category for osteoporosis.
Aspartame has not been shown to be a carcinogen in any reputable, peer-reviewed study. One commenter referred to "aspartame poisoning"? Maybe if you're phenylketonuric. Otherwise ... nope, just more myth mongering.
If someone listed half the naturally occurring chemicals in a fresh apple, to the uneducated, that'd sound every bit as scary as the ingredient label on a diet soda can.