The U.S. Department of Labor's Occupational Safety and Health Administration issued the citations Friday for four separate incidents late last year that resulted in injuries to the cast.
The three citations carry $12,600 in proposed fines — a tiny percentage of the $65 million musical's weekly costs.
OSHA alleges that 8 Legged Productions LLC exposed the cast "to the hazards of falls or being struck during flying routines," among other charges.
A spokesman for the musical didn't immediately return calls for comment.
Injuries to four cast members — including a 35-foot fall that left one with a skull fracture and cracked vertebrae — have marred the production.