You're not digging the Panama Canal in 1911, so neither property nor people should be damaged in the course of construction. In fact, as you probably know, the Occupational Safety and Health Administration (OSHA) has specific and strict rules governing safety in many workplaces, with special rules for construction sites [source: OSHA]. These standards cover everything from sprains and strains in construction laying bricks to the personal protective equipment required of construction workers. For example, workers should have fall protection for any work done above 6 feet (1.8 meters) off the ground, and all workers should wear appropriate footwear.
Your contractor should follow these guidelines and make sure his or her workers comply, as well. If you see unsafe behavior on the job site, it's almost certain your contractor has seen it, too. Or he should have. Whichever the case, unsafe behavior is your contractor's fault and is a red flag that perhaps your time together should end.