As the link you provided mentioned, diet drinks are able to remain sweet due to the artificial sweeteners. Those same artificial sweeteners are used in many diet oriented food products as well (check out Walden Farms products). That said, there are differences in how bad the different sweeteners are, or how much we know about their long term effects.
As the answer from Yahoo alluded to, aspartame is one of products we know has bad properties. The more "en vogue" sweeteners like splenda (sucralose) and stevia are "less bad" than aspartame. That doesn't mean they are great either. I recommend looking at the Mayo Clinic article on artificial sweeteners for an overview.
My weight loss center was entirely against diet sodas because they made your body more acidic, and as a result more susceptible to getting sick. I'm not sure if that claim was pseudo science or not, but the Self Nutrition Data site has an inflammatory index which is measuring the same concept. According to the data there, diet coke and diet Pepsi have no impact on the inflammatory index.
Diet drinks, and most sodas, coffee, and tea contain caffeine. Caffeine is a diuretic if consumed in large enough quantities. Combined with the sodium content (see next paragraph) you can be thirstier after you drink the soda than before. Many people drink diet sodas in sufficient quantity for it to become a diuretic.
The last potentially bad thing from excess diet sodas is Sodium content. Coke zero seems to have fairly low sodium (30mg / 8oz of product) versus diet coke which has (40mg / 8oz of product). That said. most people drink large amounts of this, with serving sizes ranging between 16-48oz of soda. The sodium content at that point becomes a significant amount to worry about. High sodium levels are linked to hypertension (high blood pressure) as well as water retention.
At the end of the day, Water is still the ultimate diet drink. It helps you process protein better, it won't leave you dehydrated.