According to a recent audit report by the Treasury Inspector General, the IRS sent $7,219,518 in tax refunds in 2011 to what where--at least on paper--2,706 different aliens who were not authorized to work inside the United States. Unbelievably, all the funds were deposited into a single account.
In terms of strengthening fraud and theft detection, you would think that stopping this type of obvious abuse would be the "low-hanging fruit".