I heard the story on the radio today. Looking it up is not hard: http://www.nytimes.com/2016/05/31/opinion/gun-control-that-actually-works.html You can look it up too.
"Were there a lot more crimes committed with automatic weapons before the ban than after?" That's not the question I am asking. Did it work to virtually eliminate machine guns used in crimes? Yes.
Banning machine guns did not lead to banning semi-automatic weapons. So the slippery slope argument did not happen. Slippery slope is a logical fallacy. See: The Domino effect. Here is fallacy link: http://www.nizkor.org/features/fallacies/slippery-slope.html