The dark side of homeopathic potency is that any dangerous chemical, any particle of poison, is grim death. Ultra-filtered gas masks would become part of the national uniform, because inhaling even a few atoms of lead would lead to a neurotoxic demise in a world where homeopathic principles are true. The old medical adage that pretty much everything is carcinogenic at some level would dominate new information campaigns about safe breathing habits. Would-be poisoners would become the most devious of murderers when a lethal dose of arsenic is measured in yottagrams.
Drunkards would have the time of their lives in a world where homeopathy worked. Ethanol diluted in water in any amount makes the drink a spirit. The lower the alcoholic content the better. You would need a microscope to find a drunkard’s flask.