Potato guns are not federally regulated in the United States, and laws vary widely in states and counties, according to Wikipedia. The guns are illegal to own by anyone under age 16 in New York.
The Chicago Tribune reports that there is little data on use of potato guns or resulting injuries. However, several accidents make headlines each year. Some advocates of the weapons note that if used properly, the guns present no more danger than skateboards. However, pediatric doctor Alison Tothy told The Chicago Tribune that the guns are not well-publicized but can cause significant physical damage. She hopes hospitals start keeping statistics on injuries resulting from the guns.