Okay, before going into this, you need to ignore a couple of things:
1. The linguistic improbabilities of the movie - frankly, it's probably for the best that neither Esther Williams nor Walter Pidgeon attempted Australian accents.
2. The usual MGM staging of musical numbers - yes, there's no way that stage audiences would have seen all those angles. Just suspend your disbelief.
Once you've done that, it's a pretty good biopic. Some liberties with Annette Kellerman's story were taken, but from what I can tell it's closer to the truth than a lot of other biopics of the time.
Esther Williams, who may not have been the greatest actress ever, is really quite good in this as are the rest of her co-stars. Donna Corcoran who plays Annette as a child, is excellent.
Busby Berkeley choreographed the aquatic numbers and he's in usual form with them.