The $70 million show, which features music by U2's Bono and The Edge, closed for nearly a month so its creative team could work out technical bugs and story issues.
Its official opening night was postponed numerous times after it began previews last fall at Manhattan's Foxwoods Theatre.
Despite the custom of withholding reviews until after a show is locked and officially opens, many critics published scathing appraisals of the work-in-progress, arguing they owed it to theatergoers to warn them about what they were spending their money on. Although many of the critiques were negative, the show's producers have maintained tickets are selling well.
The New York Post said the retooled version that debuted Thursday night included an almost entirely rewritten script, additional songs and a better-defined love story. It also is closer to the original comic-book source material than the earlier incarnation of the musical was, the newspaper said.
"Welcome to all of you: ladies, gentleman and uninvited critics," the Post said lead producer Michael Cohl joked with the audience Thursday. "It's almost a brand-new show."