Thought the 1962 movie is far-better known today (though not all that well-known), the stage production was a phenomenon. As I mentioned, though it was foundationally a musical, with a score by Rodgers & Hart, it was presented as a huge extravaganza staged by the impresario Billy Rose, at the huge Hippodrome where it could be done as an actual circus, with animal acts, trapeze artists and acrobats, rather than be put on at a regular Broadway theater. And this rehearsal video shows that quite clearly. It must have been a remarkable event. The show wasn't a massive success, but ran for 233 performances which was quite respectable for that era. I suspect the stage show never built up a huge name for itself because it clearly wasn't the sort of show that could tour properly. And so the 1962 movie carries on its legacy.
The musical has some very nice songs in it, most notably three that had success outside the show, "The Most Beautiful Girl in the World," "Little Girl Blue" and the wonderful, "My Romance."
This video comes from a Paramount promotional featurette, so there's a bit of folderol at the beginning with interviews outside the theater for the show's gala premiere. (The opening of the show got a great amount of attention and was a big deal..) You can skip past that to get to the rehearsal, although there are some fun people worth checking out. Ed Wynn comes along at the :30-second mark, Fanny Brice is briefly interviewed at 1:18, and then George Burns and Gracie Allen show up at 1:58.
If you do jump to the start of the rehearsal material, that's at 2:28. Most fascinating is a segment at 3:46 where Jimmy Durante rehearses with an elephant. And hopefully he got hazard pay. There's footage here, as well, of producer Billy Rose, along with a lot of circus material and actual scenes with Durante. All in all, it's great fun and a wonderful historical document.