I saw it and really liked it a lot in Atlanta. It's hilarious, but a 3rd grader will not necessarily find it funny-- most of the jokes are at the expense of Broadway narcissists, the cast of a bus-and-truck of Godspell and a bunch of small-town, small-minded bureaucrats. All stereotypes, delivered with panache. It's all bouncy and good-natured and works a lot better than it ought to.
But if they haven't fixed the book, your 3rd grader is going to loudly ask a lot of questions like "why don't they just Google it?", "doesn't she know how to text someone?", etc etc. But I don't think there is a lot of objectionable language in it... and some nice, if heavy-handed, messages along the way about acceptance and inclusion.
In its Atlanta incarnation, The Prom seemed like it was set in the Town that Time Forgot, because even though it's supposedly 'present day', the characters (even the high schoolers) seem to understand very little about how teens share information and about how small towns really work. But that complaint aside, I think The Prom is a lot of fun....especially for Broadway fans. I hope it's fixed up a bit, that the cast stays intact from Atlanta, and that it enjoys a nice long run.