Property damage and crimes against children.
The biggest problems I see with the purge (besides the obvious) is that property damage alone would quickly mount to hundreds of millions in property losses. One building on fire without the electricity and gas cut could level an entire block in a hurry.
And I'm sorry, while all crime is legal, crimes against those 11 and under should be dealt quickly and severely. This is actually a massive plot hole, because parents, doesn't matter the society are still attached their children.