A government program set up to remove innocent people from terrorism no-fly and watch lists has been ineffective and riddled with problems, travelers and congressional leaders say.

The Department of Homeland Security's Traveler Redress Inquiry Program, or TRIP, was started almost a year ago to clear people routinely subjected to extra airport-security screening and even detention simply because their names were confused with those on the government's voluminous terrorism watch lists. The lists now contain more than 700,000...