The one that comes most immediately to mind for me is the current trouble that our (United States) economy is in. You can say that it started from a relatively small leak and that it has sunk a great ship. At any rate, it has certainly caused a lot of trouble.
The economic problems can be traced to companies giving out mortgages to people who really could not afford them. Each individual one of these mortgages was a very small leak. And you would think that mortgages in general would be pretty small compared to the US economy as a whole. But when all those mortgages got put together and when the financial companies started making derivatives based on those mortages, they turned into a really big deal.
Because of all these little leaks, the US entered a huge financial crisis back in late 2008 and has not completely recovered yet.