Current research that attempts to link diet soda with health issues[2][3] did not have equal caloric consumption. Excess caloric consumption has a direct correlation with many health issues, and in fact one of the studies[2] distinctly states:
Consequently, the previously observed diet soda–metabolic syndrome associations are generally speculated to be the result of residual confounding by other dietary behaviors, lifestyle factors, or demographic characteristics (1,2). Biological mechanisms possibly explaining these associations are few and largely focus on artificial sweeteners in beverages/foods increasing the desire for (and consumption of) sugar-sweetened, energy-dense beverages/foods (3) or disrupting consumers' ability to accurately estimate energy intake and remaining energy needs (4). Thus, diet soda consumption may result in overconsumption, increased body weight, and consequent metabolic dysfunction.
As all current research has found diet soda sweeteners to be safe per se, a tentative conclusion is that diet soda is harmless when paired with an otherwise controlled diet; many people who have bad diets consume diet soda in an attempt to do "less damage" - this results in an incorrect conclusion that diet soda leads to an unhealthy condition.