I know there are plenty of healthier options, but is diet soda (coke zero, diet dr pepper) actually bad for my health?

Multiple reasons. : A harvard study showed that diet sodas caused decline in kidney function due to the diet sweeteners. They can rot teeth and destroy teeth enamel due to being acidic in nature. Diet sodas also contain chemical substances which can cause cell damage. Although diet sodas contain low calories they still increase the size of peoples waistlines and contribute to metabolic syndrome.

Yes: Regularly drinking soda has been linked to metabolic syndrome. increased weight, decreased bone mineral density (BMD) obesity, erosion of tooth enamel, mineral depletion & dehydration. If it contains artificial sweeteners & is used daily, this is linked to a 3 fold ^ in dementia & stroke.