Is diet soda bad for you? Can it still make you put on weight?

Diet soda is ok. Diet soda is not "bad", but water is purer and better. Diet soda has artificial sweeteners, which some people worry are not good for the body, while other people feel they are not harmful. Diet soda tastes sweet to our tongues, and perhaps to our stomachs, if there are sweetness sensors down there. So, one maintains a "sweet tooth" and still crave sweets, which can lead to weight gain from snacks.
Depends on which one. Some people cannot tolerate aspartame and can make them feel ill or contribute to migraines. Stevia is tolerated well in most individuals and is in some diet soda.