I agree that the Weierstrass function is different. I felt a tinge of guilt when I included the Weierstrass function. But I included it since it's probably the most famous pathology.

That being said, I don't quite understand the distinction you're making between a practical and a conceptual pathology. The distinction I would make between the Weierstrass and the other two is that the Weierstrass is something which is just counter-intuitive whereas the other two can be used as a reason to reject the entire theory. They are almost antithetical to the purpose of the theory. Is that what you were getting at?