A number of cast members have been hurt in accidents during rehearsals and preview shows for the production.
Of a fall experienced by Spider-Man double Christopher Tierney, choreographer Daniel Ezralow told The Guardian: "He wasn't hooked up.
"Every injury has been the result of human error. There hasn't been one fault in the fly system - not one breakage in the material.
"It's like someone dropped a bucket of cement from a renovation and hit someone in the street. Thankfully, Chris was experienced enough to make a safety roll."
He added: "You can break your ankle by slipping on a wet spot, it happens to dancers every day.
"Of course, accidents that occur while you're flying across the stage are more newsworthy, but it's ridiculous for people to write that [director] Julie Taymor should be stopped and the show cancelled."