What does he mean when he refers to factories as nurseries of diease and vice

It's a metaphor, darling. A nursery (whether it's a plant nursery or a nursery school) is a place where small plants or human beings are carefully nutured so that they can grow. "He" (whoever this mysterious "he" is that you're referring to) is asserting that factories are places where bad things like "disease and vice" can similarly grow and flourish.

We need to see the poster