I can't think of another musical that ran over 1500 performances and was a huge commercial success and yet had a book that was quite inferior to the play it was based on. Apparently it was Angela Lansbury's spectacular star-making performance, the excellent score, and the fine supporting performances of Arthur, Connell, and Michaels that made the show such a big hit. When it was revived in '83 with Lansbury and 3 others from the original cast, it was a quick failure. When I saw my first production of Mame in '94, I was surprised that the book was nowhere near as good as the film.
My first experience with the show was shortly after college, as rehearsal pianist for a local production. I was familiar enough with the major songs before that, but didn't know the book at all. I remember the first night read-through (those dreadful nights where the director makes the cast slog through the songs they haven't learned yet - ugh) and I was really surprised at how lacking the book seemed. Working on the show, I gained even more appreciation for the score (except for one dreadful song), but ugh - that book really doesn't stand up well.