Well, I think Mario is actually a parody of the standard Italian stereotype, rather than a stereotype himself, similar to how Duke Nukem is a parody of the stereotypical action hero tough guy, rather than one meant to be taken seriously. I think that if Mario's powerups were pizzas and he had Mafia connections, then it would be less inoffensively cartoonish and actually offensive.
There, case closed. He's a stereotype parody, not an actual stereotype.