The widespread, severe flooding in the Midwest over the last month has exposed the vulnerabilities in a levee system that is now so full of holes that many here ruefully describe it as “Swiss cheese.” With dozens of costly breaks across Nebraska, Iowa, Missouri and nearby states, the surging waters have left large areas without even cursory flood protection. “Breaches everywhere: multiple, multiple breaches,” said Tom Bullock, the top elected official in Holt County, Mo., where crews were rushing last week to patch a leaking levee that, if it failed completely, would flood the small town of Fortescue. And with the fear of more floods in the coming years — and perhaps even the coming weeks — many people said living and farming near the water might not be viable much longer without major changes.