I like this argument which only looks at very long term statistics. Violent crime has been decreasing since colonial times if not earlier and globally. In this sense, a particular decrease in violent crime doesn't explanation as such (though the long term trend does. Perhaps lead exposure has been decreasing for a long time, perhaps not). Increases in crime, long term, are correlated roughly with veterans returning from war.

See this link for the argument.

http://blogs.berkeley.edu/2010/06/16/a-crime-puzzle-violent-...

Edit: also the original lead argument pretty hinges on a single moment of crime increase. I don't see how more detailed studies of the correlation could be more revealing since reality only provides one instance of a potential to leaded gasoline and reality is going to be noisy.